- f=Convergents[Sqrt[3]+Sqrt[7],30]
- Denominator@f
- Numerator@f
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\[\left\{4,\frac{9}{2},\frac{13}{3},\frac{22}{5},\frac{35}{8},\frac{162}{37},\frac{197}{45},\frac{3905}{892},\frac{8007}{1829},\frac{51947}{11866},\frac{59954}{13695},\frac{291763}{66646},\frac{2685821}{613509},\frac{5663405}{1293664},\frac{25339441}{5788165},\frac{31002846}{7081829},\frac{56342287}{12869994},\frac{200029707}{45691811},\frac{456401701}{104253616},\frac{656431408}{149945427},\frac{2425695925}{554089897},\frac{5507823258}{1258125221},\frac{7933519183}{1812215118},\frac{13441342441}{3070340339},\frac{21374861624}{4882555457},\frac{12859733178465}{2937486169996},\frac{38600574397019}{8817341065445},\frac{51460307575484}{11754827235441},\frac{244441804698955}{55836650007209},\frac{295902112274439}{67591477242650}\right\}\]
\[\{1,2,3,5,8,37,45,892,1829,11866,13695,66646,613509,1293664,5788165,7081829,12869994,45691811,104253616,149945427,554089897,1258125221,1812215118,3070340339,4882555457,2937486169996,8817341065445,11754827235441,55836650007209,67591477242650\}\]
\[\{4,9,13,22,35,162,197,3905,8007,51947,59954,291763,2685821,5663405,25339441,31002846,56342287,200029707,456401701,656431408,2425695925,5507823258,7933519183,13441342441,21374861624,12859733178465,38600574397019,51460307575484,244441804698955,295902112274439\}\] |