# Math Olympiad Help

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I have to find all square numbers ending in 3 4s. The first number, that has a square ending in 3 4s is 38.

Here is the given solution to the problem:

Can someone explain to me how this person got to that solution of N = 500k +/- 38?

Here is the given solution to the problem:

Can someone explain to me how this person got to that solution of N = 500k +/- 38?

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#2

(Original post by

I have to find all square numbers ending in 3 4s. The first number, that has a square ending in 3 4s is 38.

Here is the given solution to the problem:

Can someone explain to me how this person got to that solution of N = 500k +/- 38?

**WassupLadz**)I have to find all square numbers ending in 3 4s. The first number, that has a square ending in 3 4s is 38.

Here is the given solution to the problem:

Can someone explain to me how this person got to that solution of N = 500k +/- 38?

N +/- 38 is divisible by 500

So N = 500k +/- 38

Where k is the quotient and +/-38 the remainder (if we allow the remainder to be negative)

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#4

(Original post by

I don't get how and why N +/- 38 is divisible by 500

**WassupLadz**)I don't get how and why N +/- 38 is divisible by 500

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(Original post by

Which parts do you understand up to?

**mqb2766**)Which parts do you understand up to?

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#6

(Original post by

I don't understand anything that he did. If you can explain it all that would be great.

**WassupLadz**)I don't understand anything that he did. If you can explain it all that would be great.

At least break it up into chunks which you're happy/unhappy with and be clear about which parts you're not clear about.

Last edited by mqb2766; 4 weeks ago

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(Original post by

You must understand some parts? Not sure I can give a totally different take on the model solution. Also the question is missing and it looks like the first part of the model solution isn't attached.

At least break it up into chunks which you're happy/unhappy with and be clear about which parts you're not clear about.

**mqb2766**)You must understand some parts? Not sure I can give a totally different take on the model solution. Also the question is missing and it looks like the first part of the model solution isn't attached.

At least break it up into chunks which you're happy/unhappy with and be clear about which parts you're not clear about.

I understand 38 is the first number that has a square ending in 444.

I understand how he got to n -38, n + 38

Now I don't understand how he got greatest common factor as 78.

I understand the prime factorisation of 1000

Why did he use the prime factorisation?

I also don't understand why he said N is 500k +/- 38, where did he get 500 from? He used 3 5s which I understand but why not 3 2s?why only 2 2s?

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#8

(Original post by

Ok so I understand the question.

I understand 38 is the first number that has a square ending in 444.

I understand how he got to n -38, n + 38

Now I don't understand how he got greatest common factor as 78.

I understand the prime factorisation of 1000

Why did he use the prime factorisation?

I also don't understand why he said N is 500k +/- 38, where did he get 500 from? He used 3 5s which I understand but why not 3 2s?why only 2 2s?

**WassupLadz**)Ok so I understand the question.

I understand 38 is the first number that has a square ending in 444.

I understand how he got to n -38, n + 38

Now I don't understand how he got greatest common factor as 78.

I understand the prime factorisation of 1000

Why did he use the prime factorisation?

I also don't understand why he said N is 500k +/- 38, where did he get 500 from? He used 3 5s which I understand but why not 3 2s?why only 2 2s?

Edit - Also is it 76 or.78 (typo?)

Last edited by mqb2766; 4 weeks ago

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#9

**WassupLadz**)

Ok so I understand the question.

I understand 38 is the first number that has a square ending in 444.

I understand how he got to n -38, n + 38

Now I don't understand how he got greatest common factor as 78.

I understand the prime factorisation of 1000

Why did he use the prime factorisation?

I also don't understand why he said N is 500k +/- 38, where did he get 500 from? He used 3 5s which I understand but why not 3 2s?why only 2 2s?

HCF(N-38,76)

Is syraightforward. The HCF must divide both N+38 and N-38, so it must divide their difference. This is used repeatedly in Euclids algorithm for calculating the HCF. So the HCF must divide 76.

Is that ok?

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(Original post by

The

HCF(N-38,76)

Is syraightforward. The HCF must divide both N+38 and N-38, so it must divide their difference. This is used repeatedly in Euclids algorithm for calculating the HCF. So the HCF must divide 76.

Is that ok?

**mqb2766**)The

HCF(N-38,76)

Is syraightforward. The HCF must divide both N+38 and N-38, so it must divide their difference. This is used repeatedly in Euclids algorithm for calculating the HCF. So the HCF must divide 76.

Is that ok?

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#11

(Original post by

No, why is that true? why can't it just be 38 as the HCF?

**WassupLadz**)No, why is that true? why can't it just be 38 as the HCF?

So it will also divide into a-b. If you've gone over Euclid's HCF method, this is a central part.

As a-b=76=2^2*19 in this case, that's the maximum the HCF can be and the answer then goes into showing the HCF is 2*19.

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