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Example of vector space 2

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Example of vector space

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Theorem on multiplicative arithmetic function

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Multiplicative arithmetic function Number Theory Tamil

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Vector space Algebra Tamil

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Field Algebra Tamil

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∅(n)=∑μ(d).(nd) = n. Π (1-(1p))

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F'Mertens lemma Number Theory Tamil

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Mobius function Number Theory Tamil

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Product of d = n^[τ(n)2] where dn Number Theory Tamil

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σ(n) is odd ⇔ n is a perfect square or twice a perfect square

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τ(n) is odd ⇔ n is a perfect square Number Theory Tamil

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τ(n) and σ(n) for n=P₁^K₁.P₂^K₂...... Pᵢ^Kᵢ Number Theory Tamil

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Arithmetic Function Number Theory Tamil

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∅(mn)=n∅(m)

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∑k= 12.n∅(n) where (n,k)=1 Number Theory Tamil

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∑∅(d)=n where dn Number Theory Tamil

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Let n be an integer greater than 2 , then ∅(n) is evenNumber Theory

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∅(n)=∅(p₁^k₁)∅(p₂^k₂).....∅(pᵢ^kᵢ)

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If p is a pime and k is a positive integer, then ∅(p^k)= p^k - p^(k-1)

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∅(n)=n-1 if and only if n is a prime

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Let p be an odd prime with p=3(mod 4). Then [(p-12)!]²=1(mod p)

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For an odd prime p, x²=-1(mod p) if and only if p=1(mod 4) Tamil

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aⁿ-bⁿ=aⁿ⁻¹+aⁿ⁻²b+...+abⁿ⁻²+bⁿ⁻¹ Proof

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Wilson's Theorem proof Tamil

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Solution for x²-1=0 (mod 8) Number Theory Tamil

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f^k(m) is divisible by k! Number Theory Tamil

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Quick procedure to solve a polynomial congruence Number Theory

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Procedure to solve a polynomial congruence Proof Number Theory

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Arithmetic Inverse Number Theory Tamil

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