Difference between revisions of "1954 AHSME Problems/Problem 49"
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== Solution == | == Solution == | ||
− | Although all of the forms listed can be used to show that the difference of <math>(2a+1)^2</math> and <math>(2b+1)^2</math> is necessarily divisible by <math>8</math>, we should use <math>\boxed{\textbf{( | + | Although all of the forms listed can be used to show that the difference of <math>(2a+1)^2</math> and <math>(2b+1)^2</math> is necessarily divisible by <math>8</math>, we should use <math>\boxed{\textbf{(C)}}</math> because at least one of the second and third factors are necessarily of different parities, so that their product is necessarily even and we are done. |
== See Also == | == See Also == |
Latest revision as of 01:31, 18 September 2020
The difference of the squares of two odd numbers is always divisible by . If , and and are the odd numbers, to prove the given statement we put the difference of the squares in the form:
Solution
Although all of the forms listed can be used to show that the difference of and is necessarily divisible by , we should use because at least one of the second and third factors are necessarily of different parities, so that their product is necessarily even and we are done.
See Also
1954 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 48 |
Followed by Problem 50 | |
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