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Suppose in a sequence of positive integers every 17-sum is even and every 18-sum is odd.What is the maximum length of such a sequence ? DETAILS AND ASSUMPTIONS: Here p-sum means the sum of p consecutive numbers.

Suppose in a sequence of positive integers every 17-sum is even and every 18-sum is odd.What is the maximum length of such a sequence ? 


DETAILS AND ASSUMPTIONS:


Here p-sum means the sum of p consecutive numbers.

Grade:10

2 Answers

Shivam Dimri
43 Points
8 years ago

well you said a sequece!!!

sequences can be anything,

even repetition of the same numbers strecting to any amount 

had it been ap

then that wud be different

but YOUR PRESCRIBED SEQUENCE shud stretch to infinity!!

Adhiraj Mandal
32 Points
8 years ago

Dear Shubham,

I have already solved the problem myself.However,your solution is not correct.The maximum length is 33.Actually,if every p-sum is even and every q sum is odd,with gcd(p,q)=1,then the maximum length is (p+q-2).The proof is tricky.Write 18 consecutive 17-term sequences and check that you will reach to ODD=EVEN .................... which is a contrdiction. 

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