Question

let t be a number when it divided by 11,13and 15 leaves a remainder in the sets (7,8,9),(1,2,3)&(4,5,6) respectively.Find the sum of the squares of the digits of t.

Answer 1

Answer:

et's denote the set of required numbers by x. Let a, b & c be whole numbers.

x mod 11 = 1 so x = 11a + 1.

x mod 13 = (11a+1) mod 13 = 2.

11a mod 13 = 1 = 66 mod 13

a mod 13 = 6 mod 13 = 6.

So, a = 13b + 6.

So, x = 143b + 67.

x mod 15 =(143b+67) mod 15=3.

143b mod 15 = -64 mod 15.

143b mod 15 = 11 = 1001mod15

b mod 15 = 7 mod 15 = 7.

b = 15c + 7.

So, x = 2145c + 1068.