Divizibilitate si putere perfecta

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Filip Chindea
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Joined: Thu Sep 27, 2007 9:01 pm
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Divizibilitate si putere perfecta

Post by Filip Chindea »

Fie \( b, n > 1 \) intregi. Presupunem ca oricare ar fi \( k > 1 \) exista un intreg \( a_k \) astfel incat \( k | b - a_k^n \). Aratati ca \( b \) este o putere a \( n \)-a a unui intreg.

[ IMO Shortlist 2007, N2 ]
Life is complex: it has real and imaginary components.
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