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.

Question

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.

Shivam Dimri · Answer

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 · Answer

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.

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

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.

2 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Magical Mathematics[Interesting Approach]

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship