Guest Posted January 29, 2009 Report Share Posted January 29, 2009 (edited) "I see that our room numbers are 100 and 164," said Professor Smart. "What of it?" retorted Professor Clever. "If you add 125 to either number, you get a perfect square," replied Professor Smart. After some time, Professor Clever answered " There is an integer less than 125 that does the same thing." "You are wrong," said Professor Smart. Who was right Professor Smart or Professor Clever? 164-100=64 You need a pair of perfect squares that lower than 100+125=225 and 164+125=289, that also differ by 64. There are two such pairs: 0 and 64, 36 and 100. The two integers lower than 125 would be -100 and -64. Professor Clever was right Edited January 29, 2009 by Kevin_3.1415 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 29, 2009 Report Share Posted January 29, 2009 -100 and -64 do the trick. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 29, 2009 Report Share Posted January 29, 2009 -100 and -64 do the trick. Good Job! Most of the time people only look for the positive ones. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 29, 2009 Report Share Posted January 29, 2009 If he had used the term natural number instead of integer, the other would have been right. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 29, 2009 Report Share Posted January 29, 2009 "I see that our room numbers are 100 and 164," said Professor Smart. "What of it?" retorted Professor Clever. "If you add 125 to either number, you get a perfect square," replied Professor Smart. After some time, Professor Clever answered " There is an integer less than 125 that does the same thing." "You are wrong," said Professor Smart. Who was right Professor Smart or Professor Clever? 164-100=64 You need a pair of perfect squares that lower than 100+125=225 and 164+125=289, that also differ by 64. There are two such pairs: 0 and 64, 36 and 100. The two integers lower than 125 would be -100 and -64. Professor Clever was right -64 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 29, 2009 Report Share Posted January 29, 2009 "I see that our room numbers are 100 and 164," said Professor Smart. "What of it?" retorted Professor Clever. "If you add 125 to either number, you get a perfect square," replied Professor Smart. After some time, Professor Clever answered " There is an integer less than 125 that does the same thing." "You are wrong," said Professor Smart. Who was right Professor Smart or Professor Clever? 164-100=64 You need a pair of perfect squares that lower than 100+125=225 and 164+125=289, that also differ by 64. There are two such pairs: 0 and 64, 36 and 100. The two integers lower than 125 would be -100 and -64. Professor Clever was right You could add -100 making 100 zero and 164, sixty four. Professor Clever is right. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 29, 2009 Report Share Posted January 29, 2009 "I see that our room numbers are 100 and 164," said Professor Smart. "What of it?" retorted Professor Clever. "If you add 125 to either number, you get a perfect square," replied Professor Smart. After some time, Professor Clever answered " There is an integer less than 125 that does the same thing." "You are wrong," said Professor Smart. Who was right Professor Smart or Professor Clever? 164-100=64 You need a pair of perfect squares that lower than 100+125=225 and 164+125=289, that also differ by 64. There are two such pairs: 0 and 64, 36 and 100. The two integers lower than 125 would be -100 and -64. Professor Clever was right This might just be me, but Clever says he knows an integer less than 125 that if you add 125 to you get a perfect square. Ok, Did we not just mention 100, he never said distinct of integer pair, one number, under 125, that exhibits taht property. It works Quote Link to comment Share on other sites More sharing options...
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"I see that our room numbers are 100 and 164," said Professor Smart.
"What of it?" retorted Professor Clever.
"If you add 125 to either number, you get a perfect square," replied Professor Smart.
After some time, Professor Clever answered " There is an integer less than 125 that does the same thing."
"You are wrong," said Professor Smart.
Who was right Professor Smart or Professor Clever?
Edited by Kevin_3.1415Link to comment
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