Find all natural numbers a , b , c such that a &#x2264;<!-- ≤ --> b &#x2264;<!-

Daphne Fry

Daphne Fry

Answered question

2022-05-15

Find all natural numbers a , b , c such that a b c and a 3 + b 3 + c 3 3 a b c = 2017

Answer & Explanation

stormiinazlhdd

stormiinazlhdd

Beginner2022-05-16Added 12 answers

a 2 + b 2 + c 2 a b b c c a = 1 2 ( ( a b ) 2 + ( b c ) 2 + ( c a ) 2 ) = 1
( a b ) 2 + ( b c ) 2 + ( c a ) 2 = 2
So, two between a , b , c are equal and the other has the difference of 1 from the others.
WLOG, assume b = a and c = a ± 1 (Ignoring a b c here.).
a + b + c = 3 a ± 1 = 2017 = 3 × 672 + 1
Thus c = a + 1 a = b = 672 and c = 673

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?