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How to find minimum $T= a+b+(a-b)(c-b)$ for $ab+bc+ca=3.$

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#inequality #sums-of-squares #buffalo-way
67
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What is min $T=\sqrt{\frac{1-bc}{2b^2+5bc+2c^2}}+\sqrt{\frac{1-ac}{2a^2+5ac+2c^2}}+\sqrt{\frac{1-ba}{2b^2+5ba+2a^2}}$

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#inequality #cauchy-schwarz-inequality #sums-of-squares #uvw
28
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On divisors of $N$ appearing in the set of curvatures of an Apollonian gasket

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#elementary-number-theory #circles #factoring #sums-of-squares
65
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Sum of square of parts, and sum of binomials over integer partition

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#combinatorics #summation #upper-lower-bounds #integer-partitions #sums-of-squares
142
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Sums of squares using the circle method

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#number-theory #analytic-number-theory #sums-of-squares
116
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Asymptotic growth of sum-of-two-squares function

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#number-theory #elementary-number-theory #sums-of-squares
146
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Sum of three rational squares is the sum of their reciprocals

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#quadratics #quaternions #sums-of-squares
138
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Factorisation of the sum of $n$ squares using hypercomplex numbers

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#complex-numbers #factoring #sums-of-squares #hypercomplex-numbers
55
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Sum of squares $\pmod p$

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#elementary-number-theory #modular-arithmetic #sums-of-squares
180
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Show that the sum is between (1,2)

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#sequences-and-series #upper-lower-bounds #sums-of-squares
76
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How do I calculate the prediction interval for a data set in python?

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#statistics #python #sums-of-squares #mean-square-error
27
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Finding $\sin(a+b)^{2k} = \sum a_i \sin^{2 n_i}(b_i a) \cos^{2 m_i}(c_i a) \sin^{2 l_i}(d_i b) \cos^{2 j_i}(e_i b)$

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#trigonometry #closed-form #sums-of-squares
76
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Derivation of $SSE =S_{yy} - S_{xy}^2/S_{xx}$

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#regression #variance #covariance #linear-regression #sums-of-squares
714
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Odd square as sum of $9$ distinct odd squares

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#elementary-number-theory #square-numbers #sums-of-squares
99
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If the sum of four squares is a square, what is the equivalent sum of three squares?

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#elementary-number-theory #reference-request #diophantine-equations #sums-of-squares

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