Question

x1,x2,x3,....x10 are integers,none of which are divisble by 3.the remainder when x1^2+x2^2+x3^2....+x10^2 is divisible by 3 is ____ ?

Answer 1

Answer: 1

Step-by-step explanation:

Since the integers aren't divisible by 3, they are of the form 3n + 1 or 3n - 1.

So x² = (3n + 1)² or (3n - 1)²

x² = 9n² + 1 + 6n or 9n² + 1 - 6n

Taking 3 common,

3(n² + 2n) + 1 and 3(n² - 2n) + 1

Therefore remainder is 1.

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