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Old 2021-05-08, 00:09   #1
Charles Kusniec
 
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Aug 2020
Brasil

610 Posts
Default A pretty good challenge

A PGC (pretty good challenge). Given:

x=(y^2-(n^2-n))/(2n-1)=(y^2-Oblong)/Odd

To prove,

1. If n>0, there will be Integer solution for x iff (2n-1) are the numbers that are divisible only by primes congruent to 1 mod 4 (http://oeis.org/A004613, https://oeis.org/A008846, https://oeis.org/A020882).

2. If n≤0, there will be Integer solution for x iff n=-|2m| negative Even (negative sequence https://oeis.org/A226485, or twice the negative sequence http://oeis.org/A094178).
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