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What is the Remainder when 16^3 +17^3+18^3 +19^3 is devided by 70

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use the formula x3+y3 =(x+y)(x2-xy+y2)

then group 173 and 183 and 163 and 193  in both the cases x+y gives 35 take 35 as common from the entire expression the resultant expression within the bracket will be (16² - 16·19 + 19² + 17² - 17·18 + 18²) 

the entire expression evaluates to be as even and hence the original expression is divisible by both 35 and 2 and hence by 70.  So the resultant remainder is 0

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