We have 34 cakes. Each box can hold 5 cakes only. How many boxes we need to pack and how many cakes are unpacked?

Find the quotient and remainder when a is divided by b in the following a = −12, b = 5

Show that the square of an odd integer is of the form 4q + 1, for some integer q.

Find all positive integers, when divided by 3 leaves remainder 2.

A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots. Find the number of completed rows and how many flower pots are left over.

When the positive integers a, 2b and c are divided by 13, the respective remainders are 9,7 and 10. Show that a + b + c is divisible by 13.

Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4.

A positive integer when divided by 88 gives the remainder 61. What will be the remainder when the same number is divided by 11?

Prove that two consecutive positive integers are always coprime.

In the given factorization, find the numbers m and n.

Can the number 6ⁿ, n being a natural number end with the digit 5 ? Give reason for your answer.

Is 7 x 5 x 3 x 2 + 3 a composite number? Justify your answer 

' a '  and '  b ' are two positive integers such that a^b x b^a = 800. Find ' a ' and ' b'

For what values of natural number n, 4ⁿ can end with the digit 6? 

if m, n are natural numbers , for what values of m, does 2ⁿ x 5^m ends in 5?

If 13824 = 2^a x 3^b then find a and b.

Determine the value of d such that 15 \(\equiv \) 3 (mod d).

Find the least positive value of x such that
67 + x \(\equiv \) 1 (mod 4)