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  1. Prove Method of infinite Descent : square k is irrational if k is not square free

    Prove Method of infinite Descent : square k is irrational if k is not square free

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  2. sinx+sin2x+sin3x+...+sin nx, cosx+cos2x+cos3x+cos 4 x+...+cos nx

    sinx+sin2x+sin3x+...+sin nx, cosx+cos2x+cos3x+cos 4 x+...+cos nx

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  3. Prove Method of infinite Descent (Vieta's jumping) : (a^2+b^2)/(ab+1) is square, imo1988

    Prove Method of infinite Descent (Vieta's jumping) : (a^2+b^2)/(ab+1) is square, imo1988

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  4. Normal subgroup and quotient subgroup

    Normal subgroup and quotient subgroup

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  5. There exist distinct integers x,y,z for which, x^2+y^2+z^2=14^n

    There exist distinct integers x,y,z for which, x^2+y^2+z^2=14^n

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  6. a_{n+2}=5a_{n+1}-6a_{n} Mathematical induction

    a_{n+2}=5a_{n+1}-6a_{n} Mathematical induction

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  7. zero morphism and kernel and cokernel

    zero morphism and kernel and cokernel

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  9. integral of lnx ln(1-x) from 0 to 1

    integral of lnx ln(1-x) from 0 to 1

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  10. Schrodinger equation and Klein Gordan equation continuity equation

    Schrodinger equation and Klein Gordan equation continuity equation

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  12. Cauchy's theorem for the abelian group, Sylow theorem for abelian group

    Cauchy's theorem for the abelian group, Sylow theorem for abelian group

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  14. Homomorphism of ring and ideal, quotient ring

    Homomorphism of ring and ideal, quotient ring

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  17. Linear algebra advanced basic: Zorn's lemma, exchange lemma, dimension

    Linear algebra advanced basic: Zorn's lemma, exchange lemma, dimension

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  18. Integral of 1/(x^3-1) from integral of 1/(x^3+1)

    Integral of 1/(x^3-1) from integral of 1/(x^3+1)

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  19. Cayley's theorem and its generalization

    Cayley's theorem and its generalization

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  20. Group homomorphism and first group isomorphism theorem

    Group homomorphism and first group isomorphism theorem

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  21. Integral of 1/(x^2+1) by using complex number

    Integral of 1/(x^2+1) by using complex number

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  24. Inner product space and p norm

    Inner product space and p norm

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  25. Probability solution: A Total of n balls, number of 1 through n...

    Probability solution: A Total of n balls, number of 1 through n...

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