Question 109
Let $k \gt 1$ be an integer and $p = 6k + 1$ be a prime number. Prove that for each $m = 2^p - 1$
$$
\frac{2^{m-1} - 1}{127m}
$$
is an integer. (Şahin Emrah).
$$
\frac{2^{m-1} - 1}{127m}
$$
is an integer. (Şahin Emrah).
MathNet 2008-part-04 — 165 problems (EN–VI) Question 109
Math Olympiad Vault · MathNet 2008-part-04 — 165 problems (EN–VI)