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The Case of the Missing Prototype – Check the Lab’s Logbook for Suspicious Late-Night Entries
After counting the fingerprints, you turn your attention to the security logbook.It records the entry hours (from 0 to 23) of ev...
12 giorni fa
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The Case of the Missing Prototype - Count the Fingerprints Found at the Lab Door to Begin Your Investigation
You arrive at the Innovation Lab where the secret prototype was stolen. The door has been dusted for fingerprints, and a technic...
12 giorni fa
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find the nth fibonacci number
The Fibonacci sequence is defined as follows: give n, find the nth fibonacci number
12 giorni fa
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find the nth number (plus)
this problem is the harder version of Problem 61014. The numbers 2 and 7 are called lucky numbers, an integer containing only t...
12 giorni fa
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Find nth number
The numbers 2 and 7 are called lucky numbers, an integer containing only the digits 2 and 7 is also called lucky number. The pro...
12 giorni fa
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Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...
15 giorni fa
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List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...
15 giorni fa
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Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...
15 giorni fa
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List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...
15 giorni fa
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Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...
15 giorni fa
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Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...
15 giorni fa
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Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...
15 giorni fa
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Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...
15 giorni fa
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List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...
15 giorni fa
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The Goldbach Conjecture, Part 2
The <http://en.wikipedia.org/wiki/Goldbach's_conjecture Goldbach conjecture> asserts that every even integer greater than 2 can ...
18 giorni fa
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Twins in a Window
<http://en.wikipedia.org/wiki/Twin_primes Twin primes> are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a f...
18 giorni fa
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Prime factor digits
Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a...
18 giorni fa
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Twin Primes
Twin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5,...
18 giorni fa
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Mersenne Primes vs. All Primes
A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. <https://www.mathworks.com/matl...
18 giorni fa
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Mersenne Primes
A Mersenne prime is a prime number of the form M = 2^p - 1, where p is another prime number. For example, 31 is a Mersenne prim...
18 giorni fa
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Circular Primes (based on Project Euler, problem 35)
The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. The...
18 giorni fa
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Sophie Germain prime
In number theory, a prime number p is a *Sophie Germain prime* if 2p + 1 is also prime. For example, 23 is a Sophie Germain prim...
18 giorni fa
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Find the next prime number
Find the next prime number or numbers for given n. For example: n = 1; out = 2; or n = [5 7]; out = [7 11]; ...
18 giorni fa
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Estimating Monthly Electricity Cost for a Household Appliance
You recently bought an electric kettle for your kitchen, and you want to estimate how much it costs to run every month. The kett...
18 giorni fa
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Voltage Divider Calculation
A voltage divider is a simple circuit used to obtain a reduced voltage from a higher voltage source using two resistors in serie...
18 giorni fa
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LED Current Calculation
In an electrical circuit, the current (III) flowing through an LED is determined using Ohm’s Law: Where: I is the current ...
18 giorni fa
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Inductor Energy Storage Calculation
The energy (EEE) stored in an inductor is given by the formula: Where: E is the energy in joules (J) L is the inductance in...
18 giorni fa
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Calculate Charge Using Capacitance and Voltage
The charge (Q) stored in a capacitor is given by the formula:Q=C×V where: C is the capacitance (in farads) V is the voltage (...
18 giorni fa
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Energy Stored in a Capacitor
The energy (E) stored in a capacitor is given by the formula: where: C is the capacitance (in farads) V is the voltage (in ...
18 giorni fa
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Calculate Current in a Series Circuit Using KVL
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop is zero. Given a voltage source (V) and three...
18 giorni fa
