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I came across something from the higher classes of math and I tried to prove it:

What do you call this kind of reasoning. Can it be called a proof? Or is this kind of like a pseudo-proof? I've never seen any proofs actually. Is my reasoning correct or is it too ugly to look at?

[The illustrations are in the figure.png file.]

Prove that adding 1 to the product of four following natural numbers results in a square number.

Example: 1*2*3*4+1 = 25 or 5*6*7*8+1 = 1681

[tex]b^2 = a_1*a_2*a_3*a_4+1[/tex]

[tex]b = \sqrt{a_1*a_2*a_3*a_4+1}[/tex]

[tex]b^2-1 = a_1*a_2*a_3*a_4[/tex]

If ([tex]a_1*a_2*a_3*a_4[/tex]) was to be a square number without adding the one (+1), we could illustrate the product of multiplication with a geometrical square [Figure

#1]. But since we need to add (+1), it means that the square is incomplete (look at [Figure #2]).

The incomplete square in [Figure #2] is calculated to b^2-1 (look at the previous definitions of (b)). How would we calculate the area like in [Figure #1]? We factorize/break out (sorry, English is not my native tongue and I don't know the English math terminology):

[tex]\frac{b^2-1}{b-1}[/tex] = (b+1) turns into [tex](b+1)(b-1) = b^2-1[/tex]

Now we see that it is incomplete (if you look at Fig. #2).

What is taken to make [Figure #2] incomplete? We look at the difference:

[tex](b^2)-(b^2-1) = -1[/tex]

If we neutralize it with (+1), we get a square number:

[tex]b^2-1+1 = b^2[/tex]

Besides, we know that adding +1 makes b^2 a square number (look at the third definition of b):

[tex]b^2-1+1 = b^2[/tex]

ABV

What do you call this kind of reasoning. Can it be called a proof? Or is this kind of like a pseudo-proof? I've never seen any proofs actually. Is my reasoning correct or is it too ugly to look at?

[The illustrations are in the figure.png file.]

Prove that adding 1 to the product of four following natural numbers results in a square number.

Example: 1*2*3*4+1 = 25 or 5*6*7*8+1 = 1681

[tex]b^2 = a_1*a_2*a_3*a_4+1[/tex]

[tex]b = \sqrt{a_1*a_2*a_3*a_4+1}[/tex]

[tex]b^2-1 = a_1*a_2*a_3*a_4[/tex]

If ([tex]a_1*a_2*a_3*a_4[/tex]) was to be a square number without adding the one (+1), we could illustrate the product of multiplication with a geometrical square [Figure

#1]. But since we need to add (+1), it means that the square is incomplete (look at [Figure #2]).

The incomplete square in [Figure #2] is calculated to b^2-1 (look at the previous definitions of (b)). How would we calculate the area like in [Figure #1]? We factorize/break out (sorry, English is not my native tongue and I don't know the English math terminology):

[tex]\frac{b^2-1}{b-1}[/tex] = (b+1) turns into [tex](b+1)(b-1) = b^2-1[/tex]

Now we see that it is incomplete (if you look at Fig. #2).

What is taken to make [Figure #2] incomplete? We look at the difference:

[tex](b^2)-(b^2-1) = -1[/tex]

If we neutralize it with (+1), we get a square number:

[tex]b^2-1+1 = b^2[/tex]

Besides, we know that adding +1 makes b^2 a square number (look at the third definition of b):

[tex]b^2-1+1 = b^2[/tex]

ABV

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