Question

k(a)  a  2 , find k(9) Solution: ( 9) ______________ ( 9) 9 2 ( 9) ______________        k k k

Answer 1

Answer:

If you run the Extended Euclidean Algorithm on 6363 and 2323, you'll find that 63(−4)+23(11)=163(−4)+23(11)=1. This means that 63(−28)+23(77)=763(−28)+23(77)=7 and so 63(28)+7=23(77)63(28)+7=23(77)

This means that 63(28)+7=177163(28)+7=1771 plantains were split among the 2323 travelers (each got 7777 fruits).

Where did you go wrong? I'm not sure. You didn't provide enough work to answer that. However, 6(−23)+23(7)=23≠76(−23)+23(7)=23≠7. Next, your answer of a range "t<−1.2t<−1.2 and t<−4.7t<−4.7" just doesn't make sense. The given problem is clearly looking for an integer solution - not a range of real numbers.

Step-by-step explanation:

23y = 63x + 7 becomes 23y = 7(mod 63) which reduces to y = 14(mod 63).

So y = 14 + 63t. Substituting this y into the original equation you get

x = 5 + 23t. All possible answers are given by x = 5 + 23t and y = 14 + 63t.

If you use the Extended Euclidean Algorithm you get x = 28 + 23t and

y = 77 + 63t which is the same as above if you substute t = 1.