   Chapter 2.5, Problem 30E

Chapter
Section
Textbook Problem

Prove that any positive integer is congruent to its units digit modulo 10 .

To determine

To prove: Any positive integer is congruent to its unit digit modulo 10.

Explanation

Formula used:

1) Definition: Congruence Modulo n

Let n be a positive integer, n>1. For integers x and y, x is congruent to y modulo n, if and only if xy is a multiple of n. We write xy(modn) to indicate that x is congruent to y modulo n.

2) Theorem: The Division Algorithm:

Let a and b be integers with b>0. Then, there exist unique integers q and r, such that a=bq+r with 0r<b

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