Is it possible?
Number Theory
Level
3
Find the sum of all 3 digit numbers which leave remainder 1 when divided by 4.
The answer is 123525.
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The value of these will be in the form of 4 x + 1 where 1 0 0 < 4 x + 1 < 1 0 0 0 , or 2 5 < x < 2 4 9 (round to the whole number). The first and last number satisfying this form is 101 and 997, totaling 2 4 9 − 2 5 + 1 = 2 2 5 number, hence, the sum of them is 2 2 5 × 2 1 0 9 8 = 2 2 5 × 5 4 9 = 1 2 3 5 2 5