Question

aratati ca numarul a este egal cu 1 + 5²+5⁴+.......+5³⁴ este divizibil cu 26 .
​

Answer 1

$a = 1 + 5 {}^{2} + 5 {}^{4} + ... + 5 {}^{34} \\a =1 + 5 {}^{2} + 5 {}^{4} (1 + 5 {}^{2} ) + .. + 5 {}^{32} (1 + 5 {}^{2} ) \\ a = (1 + 5 {}^{2} )(1 + 5 {}^{4} + ... + 5 {}^{32} ) \\ a = 26(1 + 5 {}^{4} + ... + 5 {}^{32} ) \\ \implies \: a \: \vdots \: 26$