Prove that among 7 positive integers, there are always two integers such that either their sun or their difference is divisible by 10. Hint: Group integers by their last digit, then group those digits by pairs that sum to 10.
Prove that among 7 positive integers, there are always two integers such that either their sun or their difference is divisible by 10. Hint: Group integers by their last digit, then group those digits by pairs that sum to 10.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 30E: 30. Prove that any positive integer is congruent to its units digit modulo .
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Prove that among 7 positive integers, there are always two integers such that either their sun or their difference is divisible by 10.
Hint: Group integers by their last digit, then group those digits by pairs that sum to 10.
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