Difference between revisions of "1985 AIME Problems/Problem 13"
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== Problem == | == Problem == | ||
| + | The numbers in the sequence <math>101</math>, <math>104</math>, <math>109</math>, <math>116</math>,<math>\ldots</math> are of the form <math>a_n=100+n^2</math>, where <math>n=1,2,3,\ldots</math> For each <math>n</math>, let <math>d_n</math> be the greatest common divisor of <math>a_n</math> and <math>a_{n+1}</math>. Find the maximum value of <math>d_n</math> as <math>n</math> ranges through the positive integers. | ||
== Solution == | == Solution == | ||
Revision as of 18:52, 10 October 2006
Problem
The numbers in the sequence 
, 
, 
, 
,
are of the form 
, where 
For each 
, let 
be the greatest common divisor of 
and 
. Find the maximum value of as ranges through the positive integers.
