Square Of ADHIRAJ !

Number Theory Level 3

Consider the equation $x^{2}+ y^{2}=2015.$ How many unordered sets of natural numbers $(x,y)$ exist?

2 0 None of the above 4

1 solution

Victor Loh
Sep 12, 2014

It suffices to observe that for any integer $a$ , $a^2 \equiv 0, 1 \pmod{4}$ . Hence $x^2+y^2 \equiv 0, 1, 2 \pmod{4}$ . Since $2015 \equiv 3 \pmod{4}$ , no such $(x,y)$ exists.

Almost a troll question. :D

Sharky Kesa - 6 years, 9 months ago

why used mod 4 instead any number ?? is there any rules or theorem ?

dark seer - 6 years, 9 months ago

the form of perfect square is (4 * k) or (4 * k) + 1, where k is an integer

search square number in wikpedia

Moh Rahmanda - 6 years, 9 months ago

You can use any mod you want, but mod 4 can prove that no such answers exist.

Samuraiwarm Tsunayoshi - 6 years, 9 months ago

then what if we use mod 2 or mod 3 instead ? but if we use that, that proof the answes exist ? I am confused too

carfin arkhels - 6 years, 9 months ago

@Carfin Arkhels – If you think that the answers exist, you should be able to give an example that actually works.

Samuraiwarm Tsunayoshi - 6 years, 9 months ago

But what is the meaning of unordered sets?

Anuj Shikarkhane - 6 years, 8 months ago

please elaborate...............

Prashant Gupta - 6 years, 8 months ago

Square Of ADHIRAJ !

1 solution

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