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 A^2 = B^3 + C^3
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 smallest integer whose first n multiples all contain a 3
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Monthly Archives: March 2016
Integers w/ 4 different partitions into 3 parts w/ the same product
Partition (number theory) https://en.wikipedia.org/wiki/Partition_(number_theory) Find integers that have 4 different partitions into 3 parts with the same product and with the same product, … Continue reading
fractional part of (6*sqrt(6) + 14)
Prove that if , then
The square of a Fibonacci number
Show that is the square of a Fibonacci number
Fibonacci numbers  is 5 F^2_{2k} + 4 always a square number?
Is always a square number? Also, is always a square number?
Fibonacci numbers  F(n) < x < F(n+1) < y < F(n+2)
If then show that is never a Fibonacci number
Fibonacci numbers – Identity
Establish the identity:
Alphametric puzzles — Part 1
Definition: An alphametic puzzle is an arithmetic problem involving words where there is a onetoone mapping between letters and digits that makes the arithmetic equation true. (1) in base 8, is a prime number Solved … Continue reading
Heron triangles & halfangle formulae
Prove that If the sides of a triangle are in arithmetic progression if and only if the cotangents of its halfangles , , are also in arithmetic progression Also, if and only if … Continue reading
a^2 + b^2 + c^2 = d^2
Prove that the product of the positive integers a and b is even if and only if there exist positive integers c and d such that … Continue reading
(2*k + 1)^2 * T(n) + T(k) is a triangular number
if is the nth triangular number then is a triangular number Hence,