# Sum of two squares equal to $2018^{2019}+2018$ [closed]

$$x^2+y^2 = 2018^{2019}+2018$$

is expressed as sum of two perfect squares.

Any pair of perfect squares can satisfy?

## closed as off-topic by Did, GNUSupporter 8964民主女神 地下教會, Isaac Browne, JMP, mathematics2x2lifeApr 29 '18 at 5:38

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, GNUSupporter 8964民主女神 地下教會, Isaac Browne, JMP, mathematics2x2life
If this question can be reworded to fit the rules in the help center, please edit the question.

• – Lord Shark the Unknown Apr 27 '18 at 10:06
• What do you mean by "any set of perfect squares can fit into this expression"? – user228113 Apr 27 '18 at 10:06
• What is the question here? – Vinyl_cape_jawa Apr 27 '18 at 10:07
• I still do not understand what the question is. – Vinyl_cape_jawa Apr 27 '18 at 10:15
• Welcome to Math.SE! Please read this post and the others there for information on writing a good question for this site. In particular, people will be more willing to help if you edit your question to include some motivation, and an explanation of your own attempts. – GNUSupporter 8964民主女神 地下教會 Apr 27 '18 at 10:16

See that your expression equals $2018(2018^{2018}+1).$ If you can do two things, you can solve your problem:
1. Express $2018$ as a sum of two squares.
Since $$1009$$ is prime and $$1009 \equiv 1 \mod 4,$$ $$100$$9 can be expressed as a sum of two squares. $$2=1^2+1^2.$$ $$2018^{2018}+1=(2018^{1009})^2+1^2.$$ From these, you can conclude that $$2 \times 1009 \times (2018^{2018}+1)$$ is a sum of two squares. (I leave to you as an exercise to prove that the product of a sum of two squares is also a sum of two squares.)