perplexus.info :: Numbers : Even and Odd Digit Numbers

Even and Odd Digit Numbers (Posted on 2023-09-08)

(A) Two different five digit base ten numbers M and N are constituted entirely by even digits.
What is the least value of M+N, given that M*N is a perfect square?

(B) Two different five digit numbers M and N are constituted entirely by odd digits.
What is the least value of M+N, given that M*N is a perfect square?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(I) (M,N) = (20402, 20000)
M*N = 20200²
M+N = 40402
(II) (M,N) = (11999,15975)
11999*15975= 13845²
11999+ 15975 = 27974
For an explanation, refer to the respective solutions submitted by Larry and Charlie here and here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
going from perfect squares to their divisors	Charlie	2023-09-08 11:37:35
Computer solution	Larry	2023-09-08 08:46:11

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