In modular arithmetic, Thue's lemma roughly states that every modular integer may be represented by a "modular fraction" such that the numerator and the denominator have absolute values not greater than the square root of the modulus. More precisely, for every pair of integers (a, m) with m > 1, given two positive integers X and Y such that X ≤ m < XY, there are two integers x and y such that a y ≡ x ( mod m ) {\displaystyle ay\equiv x{\pmod {m}}} and | x | < X , 0 < y < Y .
In modular arithmetic, Thue's lemma roughly states that every modular integer may be represented by a "modular fraction" such that the numerator and the denominator have absolute values not greater than the square root of the modulus. More precisely, for every pair of integers (a, m) with m > 1, given two positive integers X and Y such that X ≤ m < XY, there are two integers x and y such that a y ≡ x ( mod m ) {\displaystyle ay\equiv x{\pmod {m}}} and | x | < X , 0 < y < Y .
Source: Wikipedia "Thue's lemma" · CC BY-SA 4.0
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