trureturingGitHub MATHEMATICAL ATLAS

Arith / CONCEPT

A Carry Reveals the Missing Low Digits

Reading the digit of order k of a p-adic integer along the translations x, x + 1, ..., x + p^k - 1 recovers its residue modulo p^{k+1}: the first carry into that digit reveals the lower digits, and no shorter run of readings suffices.

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Carry revelation and the sharp horizon

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A Carry Reveals the Missing Low DigitsA Carry Reveals the Missing LowDigits
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Arith
Node ID
D5/S3/Arith/Congruence/CarryRevealsLowDigits
Repository path
D5/S3/Arith/Congruence/CarryRevealsLowDigits.lean
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sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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