Lifting-the-exponent lemma

The Lifting-the-exponent lemma (LTE) is a mathematical result in number theory that provides conditions under which the highest power of a prime \( p \) that divides certain expressions can be easily determined. It simplifies the computation of \( v_p(a^n - b^n) \) and related expressions, where \( v_p(x) \) denotes the p-adic valuation, which gives the exponent of the highest power of \( p \) that divides \( x \).