Question
A number when divided by 45 leaves a remainder 21. What
will be the remainder when the square of the same number is divided by 45?Solution
Let the number be N. Then, N ≡ 21 (mod 45). We are asked to find the remainder when N² is divided by 45. N² ≡ 21² (mod 45). 21² = 441. Now, divide 441 by 45: 441 ÷ 45 = 9 remainder 36. Therefore, the remainder when the square of the number is divided by 45 is 36.
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