Maths Olympiad Prep

Track / Stage 4 / 293 of 340 #553 of 1964

Problem 553

AMC 12 late, AIME early
Number theory Difficulty 5.0 Find the answer

19. In base five, there is (abb)5×(acd)5=(baeca)5(\overline{a b b})_{5} \times(\overline{a c d})_{5}=(\overline{b a e c a})_{5}, where the same letters represent the same digits, and different letters represent different digits. Then, the product of this equation converted to a decimal number is . \qquad

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

20212021

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.