Find a counterexample to show that the expression n^2 - n + 41 does not represent a prime number for all positive integers, n.
2006-12-14 08:34:29 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
n=41
41^2 - 41 + 41 = 41^2 = 41 x 41, not prime
2006-12-14 08:37:17 · answer #1 · answered by bictor717 3 · 0⤊ 0⤋
There are an infinite number of counterexamples. All values of n that equal (m * 41) will result in a composite number divisible by 41.
eg.
n = 1 * 41 = 41
--> (41)^2 - 41 + 41 = 1681 = 41 * 41
n = 2 * 41 = 82
--> (82)^2 - 82 + 41 = 6683 = 163 * 41
n = 3 * 41 = 123
--> (123)^2 - 123 + 41 = 15047 = 367 * 41
...
2006-12-15 01:41:59 · answer #2 · answered by Kookiemon 6 · 0⤊ 0⤋
41... 41² - 41 + 41 = 41² which is not a prime number.
2006-12-14 16:38:08 · answer #3 · answered by Dave 6 · 0⤊ 0⤋
n^2 - n + 41 ; n=2
4-1+41=44 not a prime #.
2006-12-14 16:36:27 · answer #4 · answered by yupchagee 7 · 0⤊ 4⤋
n = 41 is the correct answer
2006-12-14 16:38:45 · answer #5 · answered by slider 2 · 0⤊ 0⤋