[seqfan] Primes of the form (4^p+1)/5^t
David Harden
oddleehr at alum.mit.edu
Wed Mar 15 07:13:19 CET 2017
In terms of 4^n + 1, this is saying that 5^t | 4^n + 1 implies 5^(t-1) | n. To prove this, note that 4^(5k) + 1 = (4^k + 1)(4^(4k) - 4^(3k) + 4^(2k) - 4^k + 1). An easy calculation shows the latter factor is congruent to 5 modulo 25 when 5 | 4^k + 1, so it is a multiple of 5 but not a multiple of 5^2. This allows for induction on t to be used.
---- David
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