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Tasya [4]
4 years ago
14

What is the smallest positive integer $n$ for which $9n-2$ and $7n + 3$ share a common factor greater than $1$?

Mathematics
1 answer:
Goshia [24]4 years ago
6 0

Answer:

  23

Step-by-step explanation:

You can use Euler's method to find the GCF of these values:

  (9n -2) mod (7n +3) = 2n -5

  (7n +3) mod (2n -5) = n +18

  (2n -5) mod (n +18) = n -23

We want this to be zero, so n = 23. (Note that none of the other remainders are zero for any positive integer n.)

The smallest positive integer n for which (9n-2) and (7n+3) share a common factor is 23. (Their common factor is 41.)

_____

<em>Check</em>

  9(23) -2 = 205 = 5×41

  7(23) +3 = 164 = 4×41

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To find this out, we first need to see the change, is it a positive change or a negative change? Well in this case, as the temperature is increasing, we find that the change is positive. The next step we need to do, id that, how much was the change by, we can find this out by finding the absolute value of the difference of -16°F and 7°F

The absolute value means, the operations answer has to be positive, if not then it will become positive.

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