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Even and Odd Number Proofs
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Show that the sum of two even numbers is even Show that the sum of an even number and an odd number is odd Show that the sum of two odd numbers is even Show that the sum of three odd numbers is odd Show that an odd number minus an odd number is even Show that an even number minus an odd number is odd Show that an even number minus an even number is even Show that the square of an odd number is odd Show that the square of an even number is even Show that the product of an odd number and an even number is even Show that the product of two even numbers is even Show that the product of two odd numbers is odd Consecutive Number Proofs
1. Show that the sum of two consecutive numbers is always odd 2. Show that the sum of two consecutive odd numbers is always even 3. Show that the product of two consecutive even numbers is always a multiple of 4 4. Show that if you add two consecutive odd numbers the result will be a multiple of 4 5. Show that if you multiply two consecutive odd numbers then add 1, the result will be a multiple of 4 6. Show that the product of three consecutive numbers is divisible by three 7. Show that the sum of any three consecutive even numbers is divisible by six 8. The product of three consecutive even numbers is a multiple of 8 9. Make a conjecture about the sum of four consecutive numbers and then prove it 10. Show that if you add the squares of three consecutive numbers and then subtract 2 you always get a multiple of 3 Even and Odd Number Proofs
1. Show that the sum of two even numbers is even 2. Show that the sum of an even number and an odd number is odd 3. Show that the sum of two odd numbers is even 4. Show that the sum of three odd numbers is odd 5. Show that an odd number minus an odd number is even 6. Show that an even number minus an odd number is odd 7. Show that an even number minus an even number is even 8. Show that the square of an odd number is odd 9. Show that the square of an even number is even 10. Show that the product of an odd number and an even number is even 11. Show that the product of two even numbers is even 12. Show that the product of two odd numbers is odd Consecutive Number Proofs
1. Show that the sum of two consecutive numbers is always odd 2. Show that the sum of two consecutive odd numbers is always even 3. Show that the product of two consecutive even numbers is always a multiple of 4 4. Show that if you add two consecutive odd numbers the result will be a multiple of 4 5. Show that if you multiply two consecutive odd numbers then add 1, the result will be a multiple of 4 6. Show that the product of three consecutive numbers is divisible by three 7. Show that the sum of any three consecutive even numbers is divisible by six 8. The product of three consecutive even numbers is a multiple of 8 9. Make a conjecture about the sum of four consecutive numbers and then prove it 10. Show that if you add the squares of three consecutive numbers and then subtract 2 you always get a multiple of 3
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