Math Is Fun Forum

Prakash Panneer

Member

Registered: 2006-06-01

Posts: 110

Integers

a, b, c are three integers satisfying the following properties:
1. 0 < a < b < c < 10000
2. a, b, c are all perfect squares.
3. a, b, c are in Geometric Progression.
What is the maximum possible value of a ?

Last edited by Prakash Panneer (2007-08-01 04:32:34)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integers

a = b = c = 10000.

Edit: Just saw it was <, not ≤.
In that case, a = 625, b = 2500, c = 10000.

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pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Integers

a = b = c = 10000.

Edit: Just saw it was <, not ≤.
In that case, a = 625, b = 2500, c = 10000.

C is not < 10000 though mathsyperson.   How about a=576, b = 2304, and c = 9216?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integers

Ah, fair point. In that case, yours looks like the best answer.

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It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Integers

If consecutive terms in a geometric progression are perfect squares, the common ratio itself must be a perfect square. ∴

We need r > 1, but in order for a to be as large as possible, r must be as small as possible. Then try r = 2; thus c = 16n[sup]2[/sup]. The largest perfect square less than 10000 that is divisible by 16 is 96[sup]2[/sup] = 9216 = 16×576.

Hence the maximum possible value of a is 576.

Last edited by JaneFairfax (2007-08-02 07:00:39)

uche

Member

Registered: 2007-07-30

Posts: 7

Re: Integers

is dere u can add some to your friend list and how di d u put that picture there

uche

Member

Registered: 2007-07-30

Posts: 7

Re: Integers

how did u put that picture there