Prove that it is impossible to construct two different seven

enrotlavaec

enrotlavaec

Answered question

2022-06-23

Prove that it is impossible to construct two different seven digit numbers, one of which is divisible by the other, out of the digits 1,2,3,4,5,6,7 (All seven digits must be in each number)

Answer & Explanation

hofyonlines5

hofyonlines5

Beginner2022-06-24Added 12 answers

Say the numbers are x and y and y divides x.
Consider the remainder upon dividing both numbers by 9. Both leave a remainder 1 (as sum of digits leaves a remainder 1).
So x = k y where 2 k 8 is not possible.
Layla Velazquez

Layla Velazquez

Beginner2022-06-25Added 11 answers

a x = b , ( a , m ) = 1 x = b / a m o d m is the unique solution such that 0 x < m .
Now put m = 9 , i.e. cast out nines. This is a ubiquitous technique for recreational problems of this ilk.

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