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What are the connection between triangular numbers and square numbers?
One relationship is that the sum of the nth and the previous triangular numbers is equal to the nth square number.That isT(n-1) + T(n) = S(n)where T(n) is the nth triangular number and S(n) is the nth square number.
Can the sum of the first n consecutive positive integers be equal to the square of a prime number?
No, it is not possible.
What does n equal in n2 equals 225?
You are looking for the square root of 225 which is 15. (15x15=225)
Can a shape be a square a parallelogram and a rhombus all at the same time?
If all the sides are equal n measurement, yes.
Why do we test only the prime numbers less than the square root of the given number?
First, you do not. You must also test the square root of the given number. So the question should be in terms of "less than or equal to". Suppose you wish to test the number n and suppose s is the square root of n. Then s*s = n Now suppose p is factor of n, with factor pair q. so that n = p*q and, without loss of generality, assume that p ≤ q. Thus p*q = s*s so that p ≤ s ≤ q That is to say, one of the pair of factors of n will be less or equal to its square root while the other member of the factor pair will be greater or equal to the square root.
