Prove that n^2 + 3n + 5 is not divisible by 121.
ARITRA SINHA , 13 Years ago
Grade 11
Magical Mathematics[Interesting Approach]> a good problem...
1 AnswersAshwin Muralidharan IIT Madras
Last Activity: 13 Years ago
Hi Aritra,
Let us assume that n2+3n+5 is divisible by 121 for some value of n which is an integer.
So n2+3n+5 must be divisible by 11.
Hence [n2-8n+16 + 11n-11] must be divisible by 11
Or (n-4)2 + 11(n-1) must be divisible by 11.
As 11(n-1) is divisible by 11, then (n-4)2 must be divisible by 11.
Which is possible only when n-4 is divisible by 11.
Or n-4 = 11x --------(for some integer x)
or n = 4+11x
For this n, n2+3n+5 = 121x2+121x+33 = 121x(x+1) + 33.
Which gives a remainder of 33, when divided by 121. And hence cannot be divisible by 121.
And hence our assumption is incorrect.
Which means n2+3n+5, can never be divisible by 121.
Hope it helps.
Best Regards,
Ashwin (IIT Madras).
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on magical mathematics[interesting approach]
Given that (1+5x)⁴ = 1 + Px + Qx² + Rx³ +..... Find the values of P - 2Q + 3R
magical mathematics[interesting approach]
1 Answer Available
Last Activity: 2 Years ago
9 men and 15 boys working 10 hours a day can make 12 pillars in 42 days, in how many days will 12 men and 22 boys working 8 hours a day can make pillars 4 times the previous number?
magical mathematics[interesting approach]
1 Answer Available
Last Activity: 2 Years ago
In the given figure, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter, find angle PCA + angle BCQ?
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 2 Years ago
for any two sets A and B (A-B)U(B-A)U (A intersection B)
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 2 Years ago
If someone has got 150 out of 200 marks in term 1 exam and 160 out of 200 marks in term 2 exam then what is the percentage in30:70
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 3 Years ago