(a) The inverse of 1234 (mod 4321) is x such that 1234*x ≡ 1 (mod 4321). Apply Euclid's algorithm:
4321 = 1234 * 3 + 619
1234 = 619 * 1 + 615
619 = 615 * 1 + 4
615 = 4 * 153 + 3
4 = 3 * 1 + 1
Now write 1 as a linear combination of 4321 and 1234:
1 = 4 - 3
1 = 4 - (615 - 4 * 153) = 4 * 154 - 615
1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234
1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234
Reducing this leaves us with
1 ≡ -1082 * 1234 (mod 4321)
and so the inverse is
-1082 ≡ 3239 (mod 4321)
(b) Both 24140 and 40902 are even, so there GCD can't possibly be 1 and there is no inverse.
Answer:
-72
Step-by-step explanation:
Answer:
15 coops
Step-by-step explanation:
Answer:
Yes, the area is 49 cm^2
Step-by-step explanation:
Answer:
y=3/5
Step-by-step explanation:
9y+6=9+2y+2y
9y+6=9+4y
9y-4y=9-6
5y=3y=3/5
