Question

19.3. Use Korselt's Criterion to determine which of the following numbers are Carmichael numbers. (e) 8911 (b) 1235 (f) 10659 (i) 126217 (j) 162401 (c) 2821 (g) 19747 (k) 172081 (d) 6601 (l) 188461 suppose that $k$ is chosen so that the three numbers $6k + 1$, $12k + 1$, $18k + 1$ are all prime numbers. 

          19.3. Use Korselt's Criterion to determine which of the following numbers are Carmichael numbers.
(e) 8911
(b) 1235
(f) 10659
(i) 126217
(j) 162401
(c) 2821
(g) 19747
(k) 172081
(d) 6601
(l) 188461
suppose that $k$ is chosen so that the three numbers
$6k + 1$, $12k + 1$, $18k + 1$
are all prime numbers.
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19.3. Use Korselt's Criterion to determine which of the following numbers are Carmichael numbers. (e) 8911 (b) 1235 (f) 10659 (i) 126217 (j) 162401 (c) 2821 (g) 19747 (k) 172081 (d) 6601 (l) 188461 suppose that k is chosen so that the three numbers 6k + 1, 12k + 1, 18k + 1 are all prime numbers.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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19.3. Use Korselt's Criterion to determine which of the following numbers are Carmichael numbers: b1235, c2821, d6601, e8911, 10659, g19747, 126217, 162401, k172081, 188461. Let k be chosen so that the three numbers 6k+1, 12k+1, and 18k+1 are all prime numbers.
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Transcript

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00:01 Here in this question it is given that the three numbers 6k plus 1 comma 12k plus 1 comma 18k plus 1 these are the prime numbers we need to prove that their product n is equals to 6k plus 1 12 k plus 1 12 k plus 1 18 k plus 1 is a carmichael number.
01:12 So here to prove this we need to show that 6k plus 1, 12 k plus 1, 18 k plus 1 is odd composite number.
01:49 So here consider n is equals to 6 k plus 1, 12 k plus 1, 12, 12, 12, 12, k plus 1 18 k plus 1 now here so let k is equals to 1 so here we have n2b equals to 6 plus 1 12 plus 1 and here we have 18 plus 1 so here we get 7 is multiplied to 13 is multiplied to 19 so here we get a odd number and it will be a composite number 2.
02:42 Similarly, here when we take k to be equals to 2, we have that n is equals to 12 plus 1.
02:55 Here we have 24 plus 1.
02:59 Here we have 36 plus 1.
03:02 So it will be equals to 13 is multiplied to 25 is being multiplied to 37.
03:12 So here whatever we get is again a odd number since the product of odd is odd and it will be a composite number too...
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