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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
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 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Category Archives: Uncategorized
What is the number of the parking space?
Source: Hong Kong elementary school
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Pythagorean triangles – Area + shortest leg is a square
Find Pythagorean triangles in which the sum of the area and the shortest leg is a square. Here are the first three examples: … Continue reading
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Pythagorean triangle whose perimeter is p^2 and area p^3
Find a Pythagorean triangle whose perimeter is a square such that equals the area. Here are two examples: Any other example? … Continue reading
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Triangular numbers between consecutive square numbers
Let be the nth mgonal number, mgonal number with index ………. Checking up to 50 the following proposition: If there are exactly two triangular numbers between and … Continue reading
SquareFree semiprimes n, σ(n), φ(n), and σ(n) * φ(n)
is the sum of divisors function Euler’s totient function is the number of positive integers not exceeding that have no common divisors with (other than the common divisor 1). In other words, … Continue reading
Identity of two equal sums of n distinct squares
Establish the following identity:
Oblong numbers : x(x+ 1), y(y+ 1), z(z+ 1) in arithmetic progression
An Oblong number is a number which is the product of two consecutive integers, that is, a number of the form There exist infinitely many triplets of positive integers , for which the numbers … Continue reading
Fibonacci in arithmetic progression
Fibonacci numbers is defined by the recurrence relation: then, giving us all increasing arithmetic progressions formed of three terms of the Fibonacci sequence For example, Prove that there are no increasing arithmetic progressions formed of … Continue reading