Maths Olympiad Prep

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Number theory Difficulty 6.1 National olympiad Prove it

11.
a) Show that if nn is an odd perfect number, then n=pam2n=p^{a} m^{2} where pp is an odd prime and pa1(mod4)p \equiv a \equiv 1(\bmod 4).
b) Use part (a) to show that if nn is an odd perfect number, then n1(mod4)n \equiv 1(\bmod 4).

Solution

None

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