SOLUTION: Hello please help me with this question:
Prove that the multiplication of four natural consequent numbers , each one added with one is an integer square. I started this:
( x+1)
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Prove that the multiplication of four natural consequent numbers , each one added with one is an integer square. I started this:
( x+1)
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Question 843158: Hello please help me with this question:
Prove that the multiplication of four natural consequent numbers , each one added with one is an integer square. I started this:
( x+1) (x+2) (x+3) (x+4)=n^2 where n-is an integer
Thank you! Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website! What you meant to say is (x+1)(x+2)(x+3)(x+4) + 1 = n^2. A brute-force but perfectly valid solution is to write for some integers a and b and try to find a,b so that the equation is an identity. If we match the constant terms we see that b = 5. The coefficient of x^3 on the LHS is 10, so the coefficient of x^3 on the RHS must also be 10. If we were to take the x^3 coefficient on the RHS we would see that it is 2a, so 2a = 10 --> a = 5, and we have
