There is a number
.
When is divided by 7 the remainder is 1.
It can be shown as mod operator.
What is ?
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No. = 7a + 1 = 9b + 2 = 11c + 3
7a + 1 = 9b + 2 then 9b = 7a – 1 similarly 11c + 3 = 9b + 2 then 9b = 11c + 1
11c + 1 = 7a – 1 then 11c = 7a – 2 take values of a = 1, 2, ... by trial and error when a = 49
c = (49 × 7 – 2)/11 = 31
so number is either 49 × 7 + 1 = 31 × 11 + 3 = 344