Difference between revisions of "2006 UNCO Math Contest II Problems/Problem 9"

(Created page with "== Problem == Determine three positive integers <math>a,b</math> and <math>c</math> that simultaneously satisfy the following three conditions: (i) <math>a<b<c</math> (ii) Ea...")
 
(Solution)
 
(One intermediate revision by one other user not shown)
Line 11: Line 11:
  
 
==Solution==
 
==Solution==
 +
<math>a=6;b=19,c=30</math> (also <math>2-34-47</math>)
  
 
==See Also==
 
==See Also==

Latest revision as of 01:34, 13 January 2019

Problem

Determine three positive integers $a,b$ and $c$ that simultaneously satisfy the following three conditions:

(i) $a<b<c$

(ii) Each of $a+b,a+c$ and $b+c$ is the square of an integer, and

(iii) $c$ is as small as is possible.

Solution

$a=6;b=19,c=30$ (also $2-34-47$)

See Also

2006 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
Invalid username
Login to AoPS