Cans't you do them?? En garde....

Number Theory Level 3

Here are some easy problems on brilliant.....

  1. 5 2 + 3 3 + 1 3 = a 5^2+3^3+1^3= a

  2. 6 + 6 + 6 + 6 + 6... = b 6+\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6...}}}} = b

  3. 3 c + 4 c = 5 c ? 3^c +4^c=5^c? Find c c

  4. ∑ n = 1 8 n 2 = d \sum_{n=1}^8 n^2 = d

Find a + b + c + d a+b+c+d


The answer is 268.

Vaibhav Kandwal by Vaibhav Kandwal , 21, India

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3 solutions

Rama Devi
May 19, 2015

The solution for the first one is 53. The solution for the second one is 9. The solution for the third one is 2. The solution for the last one is 204. Therefore the required answer is 53 + 9 + 2 + 204 ,which is equal to 268.

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It is 268, not 263!! :P

Vaibhav Kandwal - 6 years ago

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Thanks , I changed it.

Rama Devi - 6 years ago

All of them are easy! i guess 1. doesn't req. method as it is simple addition. 2. you can take y= root(6+(root6+..... and solve it by squaring 3. is the Pythagorean triplet 4. n(n+1)(2n+1)/6 is the formula for sum of square of 1st n natural number!

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Vaibhav Kandwal
Jan 10, 2015

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