22
14 and 6
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
That happens when only one of the two integers is negative.
A counterexample to the conjecture that the sum of any two integers greater than 1 is less than their product is the pair (2, 2). The sum of these integers is 2 + 2 = 4, while their product is 2 × 2 = 4. Here, the sum equals the product, demonstrating that the conjecture does not hold for all integers greater than 1.
They are 6, 8, 10 and 12.
16
14 and 6
31
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
The numbers are 11, 13, 15 and 17.
That happens when only one of the two integers is negative.
A counterexample to the conjecture that the sum of any two integers greater than 1 is less than their product is the pair (2, 2). The sum of these integers is 2 + 2 = 4, while their product is 2 × 2 = 4. Here, the sum equals the product, demonstrating that the conjecture does not hold for all integers greater than 1.
1, 2, 3, 4, and their negatives.
They are 6, 8, 10 and 12.
The integers are 5 and 7.
The positive integers whose squares are less than 30 are 1, 2, 3, 4, and 5. This is because the squares of these numbers are 1, 4, 9, 16, and 25, respectively, all of which are less than 30. The next integer, 6, has a square of 36, which exceeds 30.
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