Other recent suggestions include:
* Show that two irrationals can add up to a rational.
* Find three whole numbers in arithmetic progression whose product is a prime.
* Find a prime that is one less than a square. Now find another.
* Show that two irrationals can add up to a rational.
* Find three whole numbers in arithmetic progression whose product is a prime.
* Find a prime that is one less than a square. Now find another.
I don't think there's an agreed upon definition of what a "whole number" is. Then again, if you're just looking for how someone reacts to such a question, I suppose it's fine, if a bit silly.
All integers, integers >= 0, integers > 0
• The positive integers
• The non-negative integers
• The integers
Natural numbers: strictly positive integers
Whole numbers: non-negative integersI have definitely come across the usage in more modern settings as well, however.
For 2, how about -3, -1 and 1.
For 3, 3 is the only example. One less than a square is n ^ 2 - 1 = (n+1)(n-1). For n=2 the answer is 3 (3*1). For n > 2 the result is clearly factorable into two numbers > 1.
2. The first is far more quickly solved by definition of the additive inverse, anyway.
Or 7, or 31, or 127.
Edit: Nevermind - I just figured these out. Makes me feel a bit dumb now. That's what I get for not doing math for a few years. I really liked the last one - got me thinking.
I know that 1 is not considered to be a prime now, but it was considered to be a prime by most mathematicians up through the 19th century, and Lehmer included it in his lists of primes as late as 1956.