# 2mid245 - 3 5 3 State and give a short proof of the...

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Name: Midterm 2, Math 245 - Fall 2010 Duration: 50 minutes To get full credit you should explain your answers. Each of the ﬁrst three questions is worth 5 points. The bonus questions is worth 3 points. 1. Find all the integer solutions ( x, y ) of the equation 19 x + 71 y = 5 . # Score 1 2 3 4 Total

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2. How many natural numbers x with x 500 have no divisor in { 2

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Unformatted text preview: , 3 , 5 } ? 3. State and give a short proof of the binomial formula. Use the binomial formula to determine the coeﬃcient of x 25 in the expansion of ( x 2-2 x 3 ) 20 . 4. Bonus Question! Prove that every set of 8 distinct integers contains a pair whose sum or diﬀerence is divisible by 12....
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2mid245 - 3 5 3 State and give a short proof of the...

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