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  1. Prove Method of infinite Descent : no nontrivial solutions x^2+y^2=3z^2

    Prove Method of infinite Descent : no nontrivial solutions x^2+y^2=3z^2

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  2. Prove Method of infinite Descent (Vieta's jumping) : (4a^2-1)^2/(4ab-1) is integer, then a=b

    Prove Method of infinite Descent (Vieta's jumping) : (4a^2-1)^2/(4ab-1) is integer, then a=b

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  3. 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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  4. 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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  5. 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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  6. Normal subgroup and quotient subgroup

    Normal subgroup and quotient subgroup

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  7. 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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  8. zero morphism and kernel and cokernel

    zero morphism and kernel and cokernel

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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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  15. Polynomial ring over rationals

    Polynomial ring over rationals

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  18. Polynomial over a commutative ring

    Polynomial over a commutative ring

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  21. Show e really exists in one page

    Show e really exists in one page

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  22. Gaussian integer and Fermat theorem

    Gaussian integer and Fermat theorem

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  23. Ring theory lecture - definition

    Ring theory lecture - definition

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  24. Counting formula in Group theory

    Counting formula in Group theory

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  25. Permutation group (Symmetric group)

    Permutation group (Symmetric group)

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