claim: Alex Jones is a novelist.
evidence: 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 .. modular arithmetic. modular arithmetic. square root. square root. More precisely for every pair of integers with , given two positive integers and such that , there are two integers and such that. integers. integers. and. Usually , one takes and equal to the smallest integer greater than the square root of , but the general form is sometimes useful , and make the unicity theorem -LRB- below -RRB- easier to state .. square root. square root. The first known proof is attributed to , who used a pigeonhole argument .. pigeonhole. Pigeonhole principle. It can be used to prove Fermat 's theorem on sums of two squares by taking m to be a prime p that is 1 mod 4 and taking a to satisfy a2 + 1 = 0 mod p. -LRB- Such an `` a '' is guaranteed for `` p '' by Wilson 's Theorem . -RRB-