Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
2³ + 3² = 2*2*2+3*3= 8+9=17
a=2,
b=3,
P= 17,
2,3,17 are all prime numbers
Answer:
Hello! answer: 4/5
Step-by-step explanation:
20 ÷ 5 = 4 25 ÷ 5 = 5 that is 4/5 therefore 4/5 is the answer because we cannot reduce any further HOPE THAT HELPS!
Answer:
90 meters
Step-by-step explanation:
From the question we are to calculate the distance that the slug can move in 60 minutes.
From the question, we know that:
20 minutes = 30 meters
60 minutes = x meters
Cross Multiply
20 minutes × x meters = 30 meters × 60 minutes
x meters = 30 meters × 60 minutes/20 minutes
x meters = 90 meters
Answer:
a = 132; b = 12; c = 36
Step-by-step explanation:
a = b + 120
b = b
c = 3b
a + b + c = 180
(substitute these into the above equation)
b + 120 + b + 3b = 180
5b + 120 = 180
-120 -120
5b = 60
/5 /5
b = 12
(substitute b back into the first equations)
a = (12) + 120 = 132
b = (12)
c = 3(12) = 36
(check: 132 + 12 + 36 = 180)
