proof question

[halcyon vapor]

"prove that a^2 + b^2 = 1000003"

how would i solve this? also what knowledge would i need in order to solve something like this

[flint hearth]

are you trying to prove that 1000003 is the sum of two squares?

[halcyon vapor]

i guess so yeah

[vernal thistle]

It is impossible to write 1000003 as sum of 2 squares

Hint: ||modulo 4||

[wooden heart]

!xy

[worn geyser]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[halcyon vapor]

whats modulo 4

[halcyon vapor]

that is the original one xd

[flint hearth]

https://www.youtube.com/results?search_query=modular+arithmetic

use that to learn what modulo and what modular arithmetic is'

once you know that, the first link I sent you essentially said:

• write a number in its prime factorization
• look for a (prime that is 3 mod 4)^(an odd number) in the prime factorization
• if you find any, the number can't be written as the sum of two squares
• if you don't find any, the number can be written as the sum of two squares

1000003 is prime
so the prime factorization of 1000003 is just 1000003^1

• 10000003 is a prime that is 3 mod 4
• 1 is odd
  so 1000003 can't be written as the sum of two squares

[halcyon vapor]

thanks

[worn geyser]

If you are done with this channel, please mark your problem as solved by typing .close

[wooden heart]

.close