Divisibility

5^6 - 1 is divisible by

5⁶ - 1 is divisible by

5
13
31
None of these

If n is any odd number greater than 1, then n(n^2 - 1) is

If n is any odd number greater than 1, then n(n² - 1) is

divisible by 24 always
divisible by 96 always
divisible by 48 always
None of these

Let N = 55^3 + 17^3 - 72^3. N is divisible by

Let N = 55³ + 17³ - 72³. N is divisible by

both 3 and 17
both 7 and 13
both 3 and 13
both 17 and 7

What will be remainder when (67^67 + 67) is divided by 68

What will be remainder when (67⁶⁷ + 67) is divided by 68?

67
63
66
1

Find the minimum integral value of n such that the division

Find the minimum integral value of n such that the division 55n/124 leaves no remainder

124
123
31
62

Let k be a positive integer such that k+4 is divisible by 7

Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

7
5
9
3

Let p be a prime number greater than 5. Then (p^2 - 1) is

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p² - 1) is

always divisible by 6, and may or may not be divisible by 12
always divisible by 24
never divisible by 6
always divisible by 12, and may or may not be divisible by 24