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p=5k+1 ∨ p=5k+2 ∨ p=5k+3∨ p=5k+4
teza
p^4=5z+1
Dowód:
(5k+1)^4=5z+1
(5k+2)^4=5m+16=5(m+3)+1
(5k+3)^4=5n+81=5(n+16)+1
(5k+4)^4=5t+256+5(t+51)+1
c.n.u.