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hi frndz...
i have a question..

How many integral solutions exist for

x1+x2+x3+....x100=100 given that, xi > -i

i solved this question and have found the answer to be 12758826.
but the answer is not correct.
could someone please help urgently with this.

approach used:-

suppose...
x1 + x2 + x3=2
where x1>=-3,
x2>=-1 &
x3>=2


now , i performed....
2-{(-3)+(-1)+(2)}=4


ie.. no: of solutions will be 5+4+3+2+1
ie..     x1          x2          x3
-3            -1           6
-3           0             5
-3             1           4
-3            2            3
-3            3            2


so 5 solutions for x1=-3;
similarly there will be 4 solutions for x1=-2;
similarly there will be 3 solutions for x1=-1;
similarly there will be 2 solutions for x1=0;
similarly there will be 1 solutions for x1=1;


so total solutions will be 15;

i applied a similar approach to the problem.
but the answer comes out to be wrong.
am i going wrong somewhere ..pls help

Edited by happygeek: fixed formatting

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Last Post by Rashakil Fol
1

I recommend translating this problem.

How many integral solutions exist for y1 + y2 + ... + y100 = 5050, where each yi > -1?

You can see that these map to solutions to your equation by letting xi = yi - (i - 1).

The resulting equation is a simple combinatorial problem, if you look at it the right way.

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