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 How high? (Posted on 2014-03-25)
What is the highest power of 2 that divides 32048-1 ?

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 of course there's brute force | Comment 2 of 4 |

list
10   A=3^2048-1:print A
20   while A @ 2=0
30      A=A//2:Pwr=Pwr+1
40   wend
50   print Pwr:print A
OK

run
1394214727062367914687352879670157072326062321139981867597622842832032482673993
27423485002476018294548027207658124580006956269122224761375615358997681237349433
78540158472910669339525528149116914201708211530794777180195470456743321146456063
91409446736353641550166933892016135940389846869161786237025783521906362517760397
42101384851474311083735102877993131212196962695464654469816719202970619252343026
64601413248554830793584726090044155569494349819195567279859637745977739263657552
38734950863399943759859765437105700914382332572284205295945574573596097236397875
19567621434999954843382100489400924995961904023259324301047965917783124275162880
51454273552815222892748384137284481025547039947184134889037943725039340156247666
40199728129756602274499881777680026614368979845341843310799503993067568180613109
48084534985374661203278436590349231431071569402389429768922180485838968764968523
57126128803806431044258528393325640457274860664015130737680025072542749684560766
2821346676098703360
13
1701922274246054583358585058191109707429275294360329428219754446816445901701651
94608746340913108269711947274973296606453804039455840773163592967526466354186320
53882029385877281908600498228902483156382094153802218237543298897391749446357499
89513484785587941345418620473652509692858699791457258590119364650764602682812985
13307354555022352397137576755362708999263870477862127038350487308313744204520296
19874772031927283683575105090385932091667907494135213964672409357882982499581973
12908875565673759472485065230841920061501870815776617792902312711909298384274749
99472194134521429252175415636475738520461308622142729859677692770731352874954688
12810392520526395132749492355083595001888476498027508409470146148729663276669514
65087558752144289885864113498144563738243383600270804822753300772787558814224987
15923504620818678226658247790953651649257286868151159385891333600877647418174467
25007481449959022270823398917633838448821851396502845138769561856131286236036091
652996420422205
OK

shows 3^2048 - 1, then the answer to the puzzle, 13, and then (3^2048 - 1) / 2^13.

 Posted by Charlie on 2014-03-25 11:06:18

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