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

  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.)

Check

  9(23) -2 = 205 = 5×41

  7(23) +3 = 164 = 4×41

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

a

step-by-step explanation: