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The following problem was suggested by John Haverhals. Many thanks. | The following problem was suggested by John Haverhals. Many thanks. | ||
You may recall that a real number is called rational if it can be written as a fraction with integers in both the numerator and denominator, otherwise it's called irrational . There are many irrational real numbers; for example, if n is any positive integer which is not a perfect square, then | You may recall that a real number is called rational if it can be written as a fraction with integers in both the numerator and denominator, otherwise it's called irrational . There are many irrational real numbers; for example, if n is any positive integer which is not a perfect square, then <m>\sqrt{n}</m> is irrational. Find two irrational numbers, a and b, so that <m>a^b</m> is an integer. | ||
{{Bpow}} | {{Bpow}} | ||
Current revision as of 08:01, 2 September 2013
The following problem was suggested by John Haverhals. Many thanks.
You may recall that a real number is called rational if it can be written as a fraction with integers in both the numerator and denominator, otherwise it's called irrational . There are many irrational real numbers; for example, if n is any positive integer which is not a perfect square, then <m>\sqrt{n}</m> is irrational. Find two irrational numbers, a and b, so that <m>a^b</m> is an integer.
Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.