perplexus.info :: Just Math : Year and Perfect Square Puzzle

Year and Perfect Square Puzzle (Posted on 2015-08-22)

Find all possible pairs (A,B) of positive integers such that:
A² + B = 2016 and, A + B is a perfect square.

*** As an extra challenge, solve this puzzle without using a computer program aided method.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

computer solution

| Comment 1 of 2

A = 32, B = 992; A^2 = 1024, A + B = 1024

For b = 1 To 2015

a2 = 2016 - b

a = Int(Sqr(a2) + 0.5)

If a * a = a2 Then

tot = a + b

sr = Int(Sqr(tot) + 0.5)

If sr * sr = tot Then

Text1.Text = Text1.Text & a & Str(b) & " " & a2 & Str(tot) & crlf

End If

Posted by Charlie on 2015-08-22 15:55:34

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info