perplexus.info :: Numbers : The number n in n^2

The number n in n^2 (Posted on 2019-04-11)

5 is in 5²=25, but 5 is at the end of 25. 10 is in 10²=100, but 100 ends in 0. What is the smallest positive integer n such that n is in n², and there is at least one nonzero digit after n in n²?

No Solution Yet Submitted by Math Man

No Rating

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

computer-assisted solution

| Comment 1 of 3

A short program finds the first number to be 3792

3792^2 = 14379264

The program (in Ruby) was:

(4..1000000).each{|n| puts [n,n**2].join(' ') if (n**2).to_s =~ /#{n}.*[1-9]/};true

output:

3792 14379264

14651 214651801

495475 245495475625

505025 255050250625

971582 943971582724

Posted by Paul on 2019-04-11 15:22:45

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info