Naughty bits of Math

Number Theory Level 3

There are $n$ numbers that cannot be expressed as the sum of $4$ pentagonal numbers. The sum of these numbers is $k$ and the product of these numbers is $p$ . $\phi(\phi(\phi(\phi(|p-k^3-4^{15}|)))) = {l}$ where $\phi$ is Euler's Totient function. Find the digit sum of $l$ .

Note : Do not program the answer

The answer is 33.

1 solution

Mohammad Farhat
Oct 16, 2018

WARNING: This is not a complete solution and it only gives you the values where it is your duty to plug them in

The numbers are

$9, 21, 31, 43, 55 \ and \ 89$

@Aaghaz Mahajan , I bet you used calculator

Mohammad Farhat - 2 years, 7 months ago

Naah........See I am acclimatized with large numbers.......I only needed a big piece of paper and hoped that the calculations won't mess up somewhere.....!!!! But yeah I used Wolfram to check which numbers are possible..........I only remembered 9 and 21.....lol

Aaghaz Mahajan - 2 years, 7 months ago

OH! I forgot that people could code!

Mohammad Farhat - 2 years, 7 months ago

@Mohammad Farhat – Nope I didnt code.........I just checked which numbers existed satisfying the criteria!!!

Aaghaz Mahajan - 2 years, 7 months ago

@Aaghaz Mahajan , I posted a new question

Mohammad Farhat - 2 years, 7 months ago

@Mohammad Farhat – Ok........solved it

Aaghaz Mahajan - 2 years, 7 months ago

Naughty bits of Math

The answer is 33.

1 solution

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