Q12 REMAINDERS

If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of

  a. 0

  b. 1

  c. 35

  d. 69

16^3 + 17^3 + 18^3 + 19^3 = 16^3 + 19^3 + 17^3 + 18^3 is divisible by (16+19)

i.e. 35 and is also divisible by (17+18) i.e. 35 as well.

So, (16^3 + 17^3 + 18^3 + 19^3) = 35x+35y,

as x+y must be even,

hence the given expression is divisible by 70.

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