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

11–13 2.0

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.

Problem #PRU-30738

Problems Number Theory Divisibility Divisibility rules Divisibility tests for 2 and 4 Methods Algebraic methods Proof by exhaustion

11–12 2.0

How many different four-digit numbers, divisible by 4, can be made up of the digits 1, 2, 3 and 4,

a) if each number can occur only once?

b) if each number can occur several times?

Problem #PRU-31276

Problems Number Theory Divisibility Divisibility rules Divisibility tests for 2 and 4

11–13 2.0

Is the number 12345678926 square?