Excel in math, science, and engineering

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Log in with Facebook Log in with Google

or

Log in with email

Join using Facebook Join using Google

or

Join using email

New user? Sign up

Existing user? Sign in

Courses

All
Fundamentals
Intermediate
Industry Applications

Topics

Algebra
Geometry
Number Theory
Calculus
Discrete Mathematics
Basic Mathematics
Logic
Classical Mechanics
Electricity and Magnetism
Computer Science
Quantitative Finance
Chemistry

Community

All

100 Day Summer Challenge

Our Principles
Testimonials

Practice math and science questions on the Brilliant iOS app. Practice math and science questions on the Brilliant Android app.

About
Help
Terms
Privacy
© Brilliant 2017

Two Square Variables?

Number Theory Level 4

Find the sum of values of \(a\) for which \((x+1991)(x+a) + 1\) is a perfect square for every integer \(x\).

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

Sign up to access problem solutions.

That seems reasonable. Find out if you're right!

Log in with Facebook Log in with Google

or

Log in with email

Join using Facebook Join using Google

or

Join using email

New user? Sign up

Existing user? Sign in

View solutions

by Mehul Arora

×

Problem Loading...

Note Loading...

Set Loading...