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What is the remainder when the sum 1 + 7 + 13 + 19 + ... + 253 + 259 + 265 + 271 is divided by 6?

 Jul 15, 2022
 #2
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sumfor(n, 1, 46, (6*n - 5))==6256  mod 6 == 4 - the remainder.

 Jul 16, 2022
 #3
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Surely, you dont want to add up all those numbers. That's ridiculous!

 

Because all the numbers leave a remainder of 1 when divided by 6, 

1 + 7 + 13... + 271 = 1 + 1 .....+1 (mod 6)

1 + 7 + 13 + ... + 271 = 46 (mod 6)

Therefore 1 + 7 + 13 + ... + 271 = 4 (mod 6)

 Jul 16, 2022

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