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a)  Let A be the set of all numbers which can be represented as the sum of three consecutive positive integers. What is the greatest common divisor of all numbers in A?

 

b) Show that the sum of 11 consecutive integers is always divisible by 11.

c) Show that the sum of 12 consecutive integers is never divisible by 12.

 Apr 25, 2019
 #1
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a - If "b" and "c" are true, then "a" should be true. That is, the sum of any 3 consecutive integers is always divisible by 3. Therefore, the GCD of all numbers in A is 3.

A = [6, 9, 12, 15, 18, 21, 24, 27] - These are the sums of first 10 numbers grouped in 3s:[1+2+3], [2+3+4], [3+4+5]......etc. As you can see their GCD is 3.

 Apr 25, 2019
 #2
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Thanks  so much! please just also help with b and c when you have a chance.

 Apr 25, 2019
 #3
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See this link for proof of "b" and "c": https://web2.0calc.com/questions/please-help-asap_86

 Apr 25, 2019

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