Problem on Divisibility of Numbers with Specific Digit Composition

Problem Statement

Given two distinct positive integers A and B, each having 2004 digits. The digits consist of 1000 digits 1, 800 digits 2, 200 digits 3, and 4 digits 4. Prove that among the two numbers A and B, one cannot be divisible by the other.

Context and Source

This problem was posted by user Thanh nguyen on May 6, 2019, on the HOC24 learning platform, categorized under Grade 9 Mathematics.

Related Questions

• Question 1: Given set A={0,1,2,3,4,5}. How many 4-digit numbers with distinct digits can be formed such that the sum of the first two digits is one less than the sum of the last two digits?
• Question 2: Using digits 1,2,3,4,5,6, how many natural numbers satisfying the conditions can be formed? a) Having 6 digits. b) Having 6 distinct digits. c) Having 6 digits and divisible by 2.
• Question 3: Given X={0,1,2,3,4,5,6}: a) How many even 4-digit numbers with pairwise distinct digits? b) How many 3-digit numbers with distinct digits divisible by 5? c) How many 3-digit numbers with distinct digits divisible by 9?
• Question 4: How many natural numbers have the property: a) Being a 2-digit even number (digits not necessarily distinct). b) Being a 2-digit odd number (digits not necessarily distinct). c) Being a 2-digit odd number with distinct digits. d) Being a 2-digit even number with distinct digits.
• Question 5: Given set A={1,2,3,4,5,6}: a) How many 4-digit numbers with distinct digits can be formed? b) How many 3-digit numbers with distinct digits divisible by 2? c) How many 5-digit numbers with distinct digits divisible by 5?

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