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How many even integers greater than 2 and less than 20 are equal to the sum of two prime numbers?
Seven of them.
What are integers less than or equal to 2?
The integers less than or equal to 2 are: {2, 1, 0, -1, -2, -3, ...}
What is a whole number less than 40?
All positive integers less than or equal to 39 are whole numbers less than 40.
How many positive integers less than 100 have the sum of their digits equal to a perfect square?
There are 20.
How many positive integers less than 2008 have an even number of divisors?
There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).
