Table of Contents
- 1 How do you prove the square of any integer is of the form 3k or 3k 1?
- 2 What forms take square of any integer?
- 3 What some integer q every odd integer is of the form?
- 4 Is the square of any positive integer of the form 4m or 4m 1 where M is any integer?
- 5 When q is some integer in which form can every positive even integer be written?
- 6 What is the general form of every positive odd integer?
- 7 Is the square of any positive integer?
- 8 How that every positive even integer is of the form 2q and that every positive odd integer is of the form 2q 1 where q is some integer?
- 9 Is 8 = 3(3) – 1 of the form 3k-1?
- 10 How can I prove that 0 is a negative integer?
How do you prove the square of any integer is of the form 3k or 3k 1?
Prove that the square of any integer a is either of the form 3k or 3k + 1 for some integer k. Answer. By the division algorithm, any integer a must have the form a = 3q + r where 0 ≤ r ≤ 2. If r = 0, then a = 3q and thus a2 = (3q)2 = 9q2 = 3(3q2), so by letting k = 3q2 we see that a2 = 3k for some integer k.
What forms take square of any integer?
Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m. ∴ square of any positive integer is of form 3m or 3m+1. Hence proved.
What some integer m every even integer is of the form?
So,For some integer m,every even integer is of the form 2m.
What some integer q every odd integer is of the form?
We know that, odd integers are 1,3,5…. So, it can be written in the form of 2q+1. When, a=2q+1 for some integer q, then clearly a is odd.
Is the square of any positive integer of the form 4m or 4m 1 where M is any integer?
According to Euclid’s division lemma: a=bq+r, 0≤r
What some integer m every odd integer is of the form?
ANSWER: Every odd number is in the form of (2m+1).
When q is some integer in which form can every positive even integer be written?
Answer: Show that every positive even integer is of the form 2q and every positive odd integer is of the form 2q + 1, where q is some integer.
What is the general form of every positive odd integer?
Hint: We have to show that every positive even integer is of the form 2n and every positive odd integer is of the form 2n+1.
How that the square of any positive integer is either of the form 4q or 4q 1 for some integer q?
Let positive integer a be the any positive integer. Then, b = 4 . 0 ≤ r < 4 , So r = 0, 1, 2, 3. Hence ,Square of any positive integer is in form of 4q or 4q + 1 , where q is any integer.
Is the square of any positive integer?
Let’s consider a positive integer ‘a’. Let b = 3, then 0 ≤ r < 3. So, r = 0 or 1 or 2 but it can’t be 3 because r is smaller than 3. Hence, it can be said that the square of any positive integer is either of form 3m or 3m + 1.
How that every positive even integer is of the form 2q and that every positive odd integer is of the form 2q 1 where q is some integer?
Let a be any positive integer and b = 2. Then, by Euclid’s algorithm, a = 2q + r, for some integer q ≥ 0, and r = 0 or r = 1, because 0≤r<2. So, a = 2q or 2q + 1. If a is of the form 2q, then a is an even integer.
Is the square of any integer of the form 3k or 3k+1?
Prove that the square of any integer is of the form 3k or 3k+1 but not of the form 3k+2. Proof: Every integer is of one of the three forms: 3k or3k+1 or 3k+2. Thus every square is of the form (3k)2or (3k+1)2or (3k+2)2.
Is 8 = 3(3) – 1 of the form 3k-1?
8 = 3(3) – 1 is of the form 3k-1, however, if 8 = 6k+5 then k = ½ which is not an integer. There is a number of the form 3k-1 that is not of the form 6k+5.
How can I prove that 0 is a negative integer?
One way to prove the result is using induction. I’ll prove it for every nonnegative integer; you need to modify the proof to show that the result applies to negative integers as well. Base: 0 is of the form 3 (0). Induction Step: There are three cases. First, suppose n is of the form 3k. Then n+1 is of the form 3k+1.
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