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21274970802584016949299731051848322146227856796515503684655248210628598374099075
38269572622296774545103747438431266995525592705 </lang>
=={{header|Julia}}==
{{works with|Julia|0.6}}
<lang julia>struct EgyptianFraction{T<:Integer} <: Real
integer::T
fractions::Vector{Rational{T}}
end
function Base.show(io::IO, fr::EgyptianFraction)
if !iszero(fr.integer)
print(io, "[$(fr.integer)] + ")
end
print(io, join(fr.fractions, " + "))
end
function Base.convert(::Type{EgyptianFraction}, fr::Rational{T}) where T
int = 0
if fr ≥ 1//1
int = floor(T, fr)
end
fr -= int
vfr = Vector{Rational{T}}(0)
while !iszero(fr)
ufr = 1 // cld(denominator(fr), numerator(fr))
push!(vfr, ufr)
fr -= ufr
end
return EgyptianFraction{T}(int, vfr)
end
Base.convert(::Type{Rational}, fr::EgyptianFraction{T}) where T =
sum(fr.fractions) + fr.integer
Base.length(fr::EgyptianFraction) = length(fr.fractions) + !iszero(fr.integer)
for fr in Rational{BigInt}[43//48, 5//121, 2014//59]
println("$fr = ", EgyptianFraction(fr))
end
function rosettatask(nmax::Integer)
frs = collect(a // b for b in big.(1:nmax) for a in 1:b-1)
efr = EgyptianFraction.(frs)
len = length.(efr)
maxlen = maximum(len)
maxfrs = frs[len .== maxlen]
println("\nEgyptian fractions with max number of terms ($maxlen): ", join(maxfrs, ", "))
denom = map(denominator ∘ last, getfield.(efr, :fractions))
maxdenom = maximum(denom)
maxfrs = frs[denom .== maxdenom]
println("\nEgyptian fraction with the maximum denominator: $(join(maxfrs, ", ")) with $maxdenom")
end
rosettatask(99)
rosettatask(999)</lang>
{{out}}
<pre>43//48 = 1//2 + 1//3 + 1//16
5//121 = 1//25 + 1//757 + 1//763309 + 1//873960180913 + 1//1527612795642093418846225
2014//59 = [34] + 1//8 + 1//95 + 1//14947 + 1//670223480
Egyptian fractions with max number of terms (8): 44//53, 8//97
Egyptian fraction with the maximum denominator: 8//97 with 579504587067542801713103191859918608251030291952195423583529357653899418686342360361798689053273749372615043661810228371898539583862011424993909789665
Egyptian fractions with max number of terms (13): 641//796, 529//914
Egyptian fraction with the maximum denominator: 36//457, 36//457, 529//914 with 839018826833450186636781520007011999269820404906753180244759299287837378895397605613261469995626498719289835112392530430840514102146998625666594756995273418015600023494049208108894185781774002683063204252356172520941088783702738286944210460710059319691268110283467445381026653628599765684739105388642310044785844902157076919003735231543781785073393176144167688252446541416466418608465458502997971425428342769433127784560570193376772878336217849260872114137931351960543608384244009505664253173875705234889570853924105640193619301332776989688248555027054395237907581951261868280899150574360164800187964167274323078311078867593844043149124596271281252530924719121766925749760855109100066731841478262812686642693395896229983745226277793055820609058348269152190083695704685769622011655159174272326647342695589818127126303038171968768650476413027459205291075571637957597356820188031655122749743652301268394542123970892422944335857917641636041892192547135178153602038877677614358281581103685526041329841496863410305888255234495015115912388514981113593387572720476744188169200130515719608747338810136728267784013352396910979904545913458536243327311977805126410065576961237640824852114328884086581542091492600312838425666927627674227053793897767395465326589843035773944346372949759909905561209334216847158156644884281300512699910530092870919061876615770708519243818676366245477462042294267674677954783726990349386117468071932874021023714524610740225814235147693954027910741673103980749749728106483987721602738673173009362802337092908847797499475895347112889339502928407808058670297722175686638678788738689803945574002805677250463286479363670076942509109589495377221095405979217163821481666646160815221224686562530536116613645305335922819524037829878961518170177968768364853399057357772141655622381280196908637031556436461404285930426436983658106288733881761514992109680298995922754466040011586713812553117621857109517258943846004179432521131844156242428351270188803919554398620084668514054504414062276012292497375238210886595006249453460414790147611422121782194848803348777061816460876697945418158442269512987729152441940326466631610424906158237288218706447963113019239557885486647314085357651895226117364760315394354624547919209138539180807829672545924239541758108877100331729470119526373928796447673951888289511964811633025369821156695934557103429921063387965046715070102916811976552584464153981214277622597308113449320462341683055200576571910241686615924531368198770946893858410058348221985603151428153382461711196734214085852523778422630907646235900752317571022131569421231196329080023952364788544301495422061066036911772385739659997665503832444529713544286955548310166168837889046149061296461059432238621602179724809510024772127497080258401694929973105184832214622785679651550368465524821062859837409907538269572622296774545103747438431266995525592705</pre>
=={{header|Kotlin}}==
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