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1. Show that there do not exist integers x and y for which 110x + 315y = 12.
2. If a and b are odd integers, prove that a2 +b2 is divisible by 2 but is NOT divisible by 4. Hint:
Any odd number can be written 2k + 1 for some integer k.
3. Prove that for any prime number p, √ p is irrational. Hint: Follow the same method that was used to prove √ 2 is irrational, by first supposing √ p can be expressed as a=b.
Verify Liouville''s formula for y^ prime prime prime -y^ prime prime - y'' + y = 0 in [0, 1]
Two commuters leave the similar city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveli
Q. How many permutations can you make of the word STATISTICS? Solution: There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'
1+3+5+7+9+11+13+15+17+19
We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f
Write down the system of differential equations for the population of both predators and prey by using the assumptions above. Solution We will start off through letting that
Case 1: Suppose we are given expressions like 3abc and 7abc and asked to compute their sum. If this is the case we should not worry much. Because adding like exp
What is Inductive Reasoning ? Sometimes we draw conclusions based on our observations. If we observe the same results again and again, we conclude that the event always has the
how to find group mean, mode and median
How a student of mathematics of b.sc can make an assignment on topic of asymptotes?
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