Problem #PRU-30611

Problems Number Theory Numeral systems Decimal number system Divisibility Divisibility rules Divisibility tests for 2 and 4

11–13 2.0

Problem

Prove that: $a_{1} a_{2} a_{3} \dots a_{n - 1} a_{n} \times 10^{3} \equiv a_{n - 1} a_{n} \times 10^{3} (\mod 4),$ where $n$ is a natural number and $a_{i}$ for $i = 1, 2, \dots, n$ are the digits of some number.

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