Square Tetrahedrals
Let T n denote the n t h tetrahdonal number. T n is a tetrahedral number that is also a perfect square. n is greater than 2 ! . T n + n = m and ϕ ( m ) = z where ϕ is Euler's Totient function.
What is the decimal value of : G C D ( ∣ T n − m 2 − z 3 ∣ , n ) where GCD ( , ) is the greatest common divisor function and ∣ ∣ is the absolute value function.
The answer is 16.
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1 solution
@Mohmmad Farhan Thanks for editing the question!!! Well it is a well known fact about the square tetrahedral numbers which I was familiar with since class 8th. So you can say that I did it without any online reference even though it was a fact I knew..... :)
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MIND=BLOWN
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Why so???!!
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@Aaghaz Mahajan – It is amazing you can remember something for so long
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@Mohammad Farhat – Hehe.......its just that I like Maths and whenever I see something cool like this, it tends to get stuck in my mind......!!!
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@Aaghaz Mahajan – I have this habit too. (That's the reason why I do not remember things I do not like)
@Aaghaz Mahajan , Can we be friends?
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Yeah!!! Why not???!! :)
Which class are you in??
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@Aaghaz Mahajan – I am Grade 4
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@Mohammad Farhat – Grade 4?????!!!! Is that 4th standard??? According to INdia???
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@Aaghaz Mahajan – I mean whta is your age instead???
@Aaghaz Mahajan – I mean in Singapore
@Aaghaz Mahajan , I recommend you to take a look at my note: π is a beautiful number
There are only 3 tetrahedral numbers that have this property, namely
T 1 = 1 2 = 1
T 2 = 2 2 = 4
T 4 8 = 1 4 0 2 = 1 9 6 0 0
Since the tetrahedral number has to be greater than 2 ! o r 2 , we choose T 4 8 .[Please do not think I play Pokemon Go]
1 9 6 0 0 + 4 8 = 1 8 8 a n d ϕ ( 1 8 8 ) = 9 2
I leave the last step to you (as I gave you the values and you can just plug them in).