odd numbers | MathCelebrity Forum

odd numbers

  1. math_celebrity

    If a is an even integer and b is an odd integer then prove a − b is an odd integer

    If a is an even integer and b is an odd integer then prove a − b is an odd integer Let a be our even integer Let b be our odd integer We can express a = 2x (Standard form for even numbers) for some integer x We can express b = 2y + 1 (Standard form for odd numbers) for some integer y a - b =...
  2. math_celebrity

    Prove there is no integer that is both even and odd

    Let us take an integer x which is both even and odd. As an even integer, we write x in the form 2m for some integer m As an odd integer, we write x in the form 2n + 1 for some integer n Since both the even and odd integers are the same number, we set them equal to each other 2m = 2n + 1...
  3. math_celebrity

    Prove the sum of two odd numbers is even

    Take two arbitrary integers, x and y We can express the odd integer x as 2a + 1 for some integer a We can express the odd integer y as 2b + 1 for some integer b x + y = 2a + 1 + 2b + 1 x + y = 2a + 2b + 2 Factor out a 2: x + y = 2(a + b + 1) Since 2 times any integer even or odd is always...
  4. math_celebrity

    if 2z-1 is an odd integer what is the preceding odd integer?

    if 2z-1 is an odd integer what is the preceding odd integer? The preceding odd integer is found by subtracting 2: 2z - 1 - 2 2z - 3
  5. math_celebrity

    n^2+n = odd

    n^2+n = odd Factor n^2+n: n(n + 1) We have one of two scenarios: If n is odd, then n + 1 is even. The product of an odd and even number is an even number If n is even, then n + 1 is odd. The product of an even and odd number is an even number
  6. math_celebrity

    n^2-n = even

    n^2-n = even Factor n^2-n: n(n - 1) We have one of two scenarios: If n is odd, then n - 1 is even. The product of an odd and even number is an even number If n is even, then n - 1 is odd. The product of an even and odd number is an even number
  7. math_celebrity

    If n represents an odd integer what represents the previous smaller odd integer

    If n represents an odd integer what represents the previous smaller odd integer Each odd integer is 2 away from the last one, so the previous smaller odd integer is found by subtracting 2 from n: n - 2
  8. math_celebrity

    2 consecutive odd integers such that their product is 15 more than 3 times their sum

    2 consecutive odd integers such that their product is 15 more than 3 times their sum. Let the first integer be n. The next odd, consecutive integer is n + 2. We are given the product is 15 more than 3 times their sum: n(n + 2) = 3(n + n + 2) + 15 Simplify each side: n^2 + 2n = 6n + 6 + 15 n^2...
  9. math_celebrity

    The sum of 5 odd consecutive numbers is 145

    The sum of 5 odd consecutive numbers is 145. Let the first odd number be n. We have the other 4 odd numbers denoted as: n + 2 n + 4 n + 6 n + 8 Add them all together n + (n + 2) + (n + 4) + (n + 6) + (n + 8) The sum of the 5 odd consecutive numbers equals 145 n + (n + 2) + (n + 4) + (n + 6)...
  10. math_celebrity

    Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages

    Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages total. The pages with photographs will have 3 or 4 photos each. How many pages has 3 photos and how many pages have 4 photos? Odd pages are 1, 3, 5, 7, 9 17/5 = 3 with 2 remaining. So all 5...
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