Want a number theory problem?

Want a number theory problem?

Posers and Puzzles

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D

Joined
25 Aug 06
Moves
0
16 Aug 09

1. Find as many triples a,b,c of positive integers as you can, that satisfy the inequalities 0 < a^2+b^2-abc <= c. You may use a computer πŸ™‚

2. Now look at the value of a^2+b^2-abc in those triples.

3. Conjecture.

4. Prove or disprove πŸ™‚

c

Joined
29 Apr 05
Moves
827
16 Aug 09

1. did that, there a lots and lots
2. did that
3. only square numbers
4. Ummmm, I'll think about that πŸ™‚

c

Joined
29 Apr 05
Moves
827
17 Aug 09

Can you do this with basic math knowledge? I have no clue what to do. πŸ™‚

D

Joined
25 Aug 06
Moves
0
17 Aug 09

Originally posted by crazyblue
Can you do this with basic math knowledge? I have no clue what to do. πŸ™‚
Yes. Nothing more than basic algebra is needed.

C

Joined
29 Jul 09
Moves
2280
18 Aug 09

What do you mean by triples?

D

Joined
25 Aug 06
Moves
0
18 Aug 09

Originally posted by CM123
What do you mean by triples?
A triple of numbers is simply three numbersπŸ™‚