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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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Monthly Archives: December 2015
(a,b); gcd(a,b) = 1; (a^2 – 5)/b and (b^2 – 5)/a are positive integers
Does there exist an infinite numbers of pairs (a, b) satisfying the given conditions?
Two Primitive Pythagorean triples
and are two primitive Pythagorean triples The primitive Pythagorean triples are characterized by and for some positive integers and , and that then For the given Pythagorean … Continue reading
Sum of a geometric series : 1 + r + r^2 + … + r^n = A^2
The general form of a geometric sequence is is the first term, and is the factor between the terms (called the “common ratio”) Find a geometric series of 3 or more positive integers, starting with 1, such … Continue reading
x^4 + y^4 = z^4 – N with (x,y,z) in arithmetic sequence
with and in arithmetic sequence. There are solutions of the form: ………. (1, 2, 3), (7, 8, 9) ………. (2, 4, … Continue reading
Average of 3^2, 4^2, 5^2, …, n^2 is itself a perfect square
Average of 1^2, 2^2, 3^2, …, n^2 is itself a perfect square
x^4 + y^4 = z^2 ± 1
Here are the solutions for all Find solutions for,
Triangles (a,b,c),(m,n,p) and (√(a^2+m^2),√(b^2+n^2),√(c^2+p^2))
Prove that if and are the lengths of the sides of two triangles then , , are also the lengths of the sides of some triangle. … Continue reading
Average of 1^2, 2^2, 3^2, …, n^2 is itself a perfect square
First few integers such that the average of is itself a perfect square
Fibonacci num3ers : a surprising occurrence
To find positive integers such that are all squares that is, Note that It happens that the first few Fibonacci numbers can be used to … Continue reading
Equation : A^2 + B^2 + 1 = C^2 + D^2 — (Part 4)
In A^2 + B^2 + 1 = C^2 + D^2 — (Part 1) and In Equation : A^2 + B^2 + 1 = C^2 + D^2 — (Part 2) We can write … Continue reading