Risolto

Easy Sequences 22: Sum of Proper Fractions
Let 'F' be the set of all proper fractions in lowest term, whose denominator is less than or equal 'd'. So, for d = 10, we have:...

28 giorni fa

Risolto

Easy Sequences 20: Counting Prime-sided Rectangles
A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-...

29 giorni fa

Risolto

Easy Sequences 19: Length of Prime-sided Rectangle with Maximum Area
A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-...

circa un mese fa

Risolto

Easy Sequences 17: Mu Variant Function
The mobius function is an important arithmetic function. It is often represented by the Greek letter mu (μ), and is sometimes ca...

circa un mese fa

Risolto

Easy Sequences 15: Pythagorean Area with maximum Hypotenuse
A pythagorean triangle is defined as a right triangle with all three sides having integer lengths. Examples of pythogorean trian...

circa un mese fa

Risolto

Easy Sequences 8: Triangles with integer sides and prime perimeters
The triangle below is special. It has integer sides and a prime perimeter. Given an integer "n" we want to know how many t...

circa 2 mesi fa

Risolto

Quadratic Congruence is a modular equation of the form: . In this exercise you will be given a vector containing the coefficie...

circa 2 mesi fa

Risolto

Easy Sequences 34: Modified Pascal's Triangle
Consider the integer triangle below: It follows the same ...

circa 2 mesi fa

Risolto

Easy Sequences 33: Web Trapped Ant
An ant is trapped on a spider web inside a can with open top. The can has a radius and height . A spider sitting on the outside...

circa 2 mesi fa

Risolto

Easy Sequences 30: Nearly Pythagorean Triangles
A Nearly Pythagorean Triangle (abbreviated as "NPT'), is an integer-sided triangle whose square of the longest side, which we wi...

circa 2 mesi fa

Risolto

Easy Sequences 26: Prime-Integer Line Segments
At the first quadrant in the -plane, you are asked to construct a line segment with the following specifications: Select a prim...

circa 2 mesi fa

Risolto

Easy Sequences 28: Sum of Radicals of Integers
The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

circa 2 mesi fa

Risolto

Easy Sequences 27: Product of Radicals of Integers
The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

circa 2 mesi fa

Risolto

Easy Sequences 31: N-N's Sequence
We define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number ...

circa 2 mesi fa

Risolto

Easy Sequences 25: Product of Series
The function 'P(n)' is defined as the series product: where 'T(n)' is the triangular sum: ...

circa 2 mesi fa

Risolto

Easy Sequences 24: Number of Coprime Lattice Points
Given a number 'n', you were tasked to mark and count all coprime lattice points at the first quadrant bounded by the points (0,...

circa 2 mesi fa

Risolto

Easy Sequences 23: Hat Guessing Game!
Consider the following Game Show: Hats, with numbers written on each, were placed on the heads of the participants. Participant...

circa 2 mesi fa

Risolto

Easy Sequences 18: Set Bits of Triple Summations
The function S(n) is defined by the following triple summations: The double brackets mean that th...

circa 2 mesi fa

Risolto

Easy Sequences 21: Combinatorial Summations
Create the function S(n), defined by the following summation: The symbol is the combination f...

circa 2 mesi fa

Risolto

Easy Sequences 16: Volume of Embedded Octahedron
An octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure). ...

circa 2 mesi fa

Risolto

Easy Sequences 13: Average Speed of Spaceship
A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ...

circa 2 mesi fa

Risolto

Easy Sequences 12: 50th Prime
Write a function that outputs the th prime after a given number . For example, the th prime after is . NOTE: If itself is pr...

2 mesi fa

Risolto

Easy Sequences 10: Sum of Cumsums of Fibonacci Sequence
The function F(n) is defined as the set of Fibonacci numbers from the first up to the n-th. S(n) is the result of applying to F,...

2 mesi fa

Risolto

Easy Sequences 9: Faithful Pairs
A "faithful number" is a non-prime number that is one less or one more than some prime number but not both. For example, for num...

2 mesi fa

Risolto

Easy Sequences 5: Project Euler Problem 1 - Again!
We are all familiar with Project Euler Problem 1. This time let's try it on bigger multiples and larger range. Find the sum of ...

2 mesi fa

Risolto

Easy Sequences 6: Coefficient sums of derivatives
Consider the polynomial function and its first-order derivative . The sums of the coefficients of P and P', are and , respecti...

2 mesi fa

Risolto

Easy Sequences 11: Factorial Digits without Trailing Zeros
Here is an easy one... It is not difficult to count the number of digits of the factorial of a given number. For example for 'n...

2 mesi fa

Risolto

Easy Sequences 4: Eliminate the Days of Confusion
If a date is written in purely numeric format some dates can be confusing, if we don't know the date format used. For example, "...

2 mesi fa

Risolto

Easy Sequences 3: Prime 44-number Squares
The positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd ...

2 mesi fa

Risolto

Easy Sequences 2: Trigonometric function with integral input and output
The function 'F', defined as: , will always return an integer if the input is a natural number (in radian...

2 mesi fa