Find the remainder if 6⁹⁹ is divided by 5.

If the polynomial 6x⁴ + 8x³ + 17x² + 21x + 7 is divided by another polynomial 3x² + 4x + 1, the remainder comes out to be ax + b. Find a and b.

A number ‘x’ when divided by 3, gives a remainder 2. The quotient when divided by 7 gives a remainder 3. The quotient is again divided by 5 and leaves a remainder of 2. What will be the remainder when x is divided by 15?

Find the remainder when 9²⁰ + 2 is divided by 4.

In a number system, on dividing 11509 by a certain number, Mukesh gets 71 as the quotient and 7 as the remainder. What is the divisor?

A number when divided by 112 it leaves 31 as remainder. When the same number is divided by 14 and 16 it leaves remainder as A and B respectively then what is the ratio of A and B?

What is the remainder when we divide 7¹¹⁰ + 11¹¹⁰ by 170?

When a number is divided by 7, it leaves 1 as the remainder. When the cube of this number is divided by 7, what will be the remainder?

When a number is divided by 13, it leaves the remainder 6. What will be the remainder when the square of the same number is divided by 13?

When 3820, 4672, and 6163 are divided by the greatest number x, the remainder in each case is the same. What is the quotient when x is divided by 1035?

What is the sum of all the numbers (greater than 100 but less than 1000) which when divided by 7, 5, and 4 gives a remainder of 3?

 If 7 divides the integer, then the remainder is 2. What will be the remainder if 9n is divided by 7?

When a positive number n is divided by 12 leaves the remainder 4, when 8n is divided by the same number, then find the remainder.

A number when divided by 8 leaves a remainder of 6, when divided by 9 leaves a remainder of 7, when divided by 10 leaves a remainder of 8. What would be sum of such numbers which are less than 1000?