Difference between revisions of "2018 UNCO Math Contest II Problems/Problem 11"
(Created page with "== Problem == == Solution == == See also == {{UNCO Math Contest box|year=2018|n=II|num-b=10|after=Last Question}} [[Category:]]") |
(→See also) |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | + | (a) Find an integer <math>n > 1</math> for which <math>1 + 2 + \ldots + n^2</math> is a perfect square. | |
| − | + | (b) Show that there are infinitely many integers <math>n > 1</math> that have the property that | |
| + | <math>1 + 2 + \ldots + n^2</math> is a perfect square, and determine at least three more examples of such <math>n</math>. | ||
| + | Hint: There is one approach that uses the result of a previous problem on this contest. | ||
== Solution == | == Solution == | ||
| − | + | <math>7</math> (Other acceptable answers are <math>41, 239, 1393, 8119</math>, and, in general, anything generated by the formula in part b. The answer students are most likely to give is <math>7</math> | |
== See also == | == See also == | ||
{{UNCO Math Contest box|year=2018|n=II|num-b=10|after=Last Question}} | {{UNCO Math Contest box|year=2018|n=II|num-b=10|after=Last Question}} | ||
| − | [[Category:]] | + | [[Category: Intermediate Number Theory Problems]] |
Latest revision as of 00:36, 14 January 2019
Problem
(a) Find an integer 
for which 
is a perfect square.
(b) Show that there are infinitely many integers that have the property that
is a perfect square, and determine at least three more examples of such 
.
Hint: There is one approach that uses the result of a previous problem on this contest.
Solution
(Other acceptable answers are 
, and, in general, anything generated by the formula in part b. The answer students are most likely to give is
See also
| 2018 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
