A proof of an assertion of Bombieri

Abstract

Following Bombieri [l]'s ideas in his work on the divisibility problem of Tn(x) by Tm(x) (2 ≤ m [less than] n) where Tn(x) = (1 + x)[to the power of n] - (1 - x)[to the power of n] - 2[to the power of n], and using the recent work of Mignotte and Waldschmidt [2] on linear forms in two logarithms, we solve this problem completely, by proving the assertion of Bombieri: T2, T3 divide every Tn T5 divides every T6k plus or minus 1, T7 divides every T6k+1, and no other cases of divisibility may occur.

Date of Award	1994
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology