This is the digit-product construction A = L + 80K, where L = {0, 1, 5, 14, 18, 19} is solution-free modulo 80 and K is witness#106 modulo 625. Since 50,000 = 80 · 625, reducing a putative relation modulo 80 forces its four low digits to be equal. Their contribution then cancels, and division by 80 leaves a relation in K modulo 625, forcing the four high digits to be equal. Hence |A| = 6 · 19 = 114.
David Renshaw · 2026-08-04 02:22:55