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Equation

x^2+xy+y^2=(x+y+3)^3/27,find all(x,y)
by aritra barua
Sat Mar 18, 2017 7:14 pm
 
Forum: Number Theory
Topic: Equation
Replies: 1
Views: 48

Re: IGO 2016 Elementary/4

It is just the official solution....is there any unique technique to solve that?
by aritra barua
Fri Mar 03, 2017 8:01 pm
 
Forum: Geometry
Topic: IGO 2016 Elementary/4
Replies: 8
Views: 221

Re: IGO 2016 Elementary/4

Isn't BC the diameter of the circumcircle?
by aritra barua
Sat Feb 25, 2017 12:33 pm
 
Forum: Geometry
Topic: IGO 2016 Elementary/4
Replies: 8
Views: 221

Re: BDMO REGIONAL 2015

Note that the distinct numbers are repeated according to their intrinsic values.Find their summation noticing that the summation of a distinct pair is equal to the square of that distinct pair.Find the remainder which shows that the division upon a number by 3 leaves the same remainder as it does up...
by aritra barua
Thu Feb 23, 2017 4:58 pm
 
Forum: Divisional Math Olympiad
Topic: BDMO REGIONAL 2015
Replies: 1
Views: 90

Re: BDMO regional 2015

For problem 10,note that SP=7 units because ST is the perpendicular bisector of triangle SPR.Apply angle bisector theorem taking PT=RT=a and PQ=b,find b=18a/7.Then apply Stewart's theorem;which mentions 324a^2/7+36a^2=16(49+63),derive a point, (24a)^2=112^2;a=14/3.Therefore,PR=2a=28/3 which takes th...
by aritra barua
Thu Feb 23, 2017 4:49 pm
 
Forum: Geometry
Topic: BDMO regional 2015
Replies: 4
Views: 117

Re: BDMO NATIONAL JUNIOR 2013/07

As per me,there won't be any fantabulous integer because at a point 1 may arrive as a fantabulous integer but it is not as 0 is not a positive integer.For this reason,the number of such integers will be 0.
by aritra barua
Wed Feb 22, 2017 8:18 pm
 
Forum: National Math Olympiad (BdMO)
Topic: BDMO NATIONAL JUNIOR 2013/07
Replies: 2
Views: 109

Re: BDMO NATIONAL JUNIOR 2012/03

Let,the total days needed by Tanvir be M1+E1,where M1 denotes the total number of mornings and E1 denotes the total number of evenings.Now,without rain,M1+E1=29.........(1),again with rain,M1+E1=11.........(2);By adding (1) and (2)..we get M1+E1=20;therefore,the total number of days to climb the mou...
by aritra barua
Wed Feb 22, 2017 2:41 pm
 
Forum: National Math Olympiad (BdMO)
Topic: BDMO NATIONAL JUNIOR 2012/03
Replies: 2
Views: 70

Re: How two altitudes determine the third

Let,ABC denote a right angled triangle.Let,the sides be 2014,1 and y units.Then the area of the triangle will be 1007 sq units.If we construct another altitude x in length,then the area will be xy/2 units.Then,we apply an equation,xy/2=1007;then x results in 2014/√(2014^2+1) units which denotes the ...
by aritra barua
Wed Feb 22, 2017 2:21 pm
 
Forum: National Math Olympiad (BdMO)
Topic: How two altitudes determine the third
Replies: 1
Views: 70

Re: BdMO 2017 junior/10

Let,the maximum number of combinations be x....which follows the form ab+ab+....+ab...where a=2,b=-1;Now,when there are 100 terms in a sequence,the numbers of combinations will be maximum when number of a=number of b.....because here distinct terms will be applicable and 2 terms are followed....In t...
by aritra barua
Fri Feb 17, 2017 9:14 pm
 
Forum: National Math Olympiad (BdMO)
Topic: BdMO 2017 junior/10
Replies: 2
Views: 74

Re: National BDMO 2017 : Junior 8

You are right,Thamim...I also feel like kicking myself for not paying much attention to this problem as I was working on other problems...or else I could have attained a bit more than being 2nd runners up......Now,This problem does need only a bit of algebraic calculations..We may let angle BAO to b...
by aritra barua
Thu Feb 16, 2017 8:51 pm
 
Forum: National Math Olympiad (BdMO)
Topic: National BDMO 2017 : Junior 8
Replies: 8
Views: 165
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