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Old 06-27-2019, 09:19 AM
Hari Seldon is offline
Join Date: Mar 2002
Location: Trantor
Posts: 12,980
There are bunches of theorems that start, "Let p be an odd prime, then ..." that fail for two. The standard proof that every number is a sum of four squares (which needs to be proved only for primes) starts out by showing that some multiple kp, with k < p, is a sum of four squares and then takes two different paths depending on whether k is odd or even.