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Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$ Follow Design: {"palette":["Paper white #FCFCFC — main background","Slate black #1E293B — primar…
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Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$ Follow Design: {"palette":["Paper white #FCFCFC — main background","Slate black #1E293B — primary text and structures","Formula blue #3B82F6 — active variables and equations","Graphite gray #64748B — secondary step explanations","Highlight gold #F59E0B — final solution highlights"],"fonts":{"STIX Two Text":"https://fonts.googleapis.com/css2?family=STIX+Two+Text:ital,wght@0,400..700;1,400..700&display=swap","Inter":"https://fonts.googleapis.com/css2?family=Inter:ital,wght@0,100..900;1,100..900&display=swap"},"type":"STIX Two Text for elegant mathematical variables and equations; Inter for highly legible sans-serif body text and proof steps.","layout":"A structured textbook grid with wide margins, centered proof blocks, and side-rail callouts for variable definitions and base conversions.","framework_treatment":"Subtle grid-line overlays resembling engineering paper, thin borders, and soft blue tinted panels for mathematical theorems.","feels_like":"A modern, high-end interactive mathematics textbook or a beautifully typeset modern LaTeX document"}