Solve lceil3^256div1000rceil-lfloor3^256^div1000rfloor

$$\lceil { 3 }^{ 256 } \div 1000 \rceil - \lfloor { 3 }^{ { 256 }^{ } } \div 1000 \rfloor$$

Evaluate

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Solution Steps

Calculate 3 to the power of 256 and get 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521.

$$\lceil \frac{139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521}{1000}\rceil -\lfloor \frac{3^{256^{1}}}{1000}\rfloor$$

Dividing 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521 by 1000 gives 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435 and remainder 521. Rewrite \frac{139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521}{1000} as 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435+\frac{521}{1000}.

$$\lceil 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435+\frac{521}{1000}\rceil -\lfloor \frac{3^{256^{1}}}{1000}\rfloor$$

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435+\frac{521}{1000} is 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436.

$$139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436-\lfloor \frac{3^{256^{1}}}{1000}\rfloor$$

Calculate 256 to the power of 1 and get 256.

$$139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436-\lfloor \frac{3^{256}}{1000}\rfloor$$

Calculate 3 to the power of 256 and get 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521.

$$139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436-\lfloor \frac{139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521}{1000}\rfloor$$

Dividing 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521 by 1000 gives 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435 and remainder 521. Rewrite \frac{139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435521}{1000} as 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435+\frac{521}{1000}.

$$139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436-\lfloor 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435+\frac{521}{1000}\rfloor$$

The floor of a real number a is the largest integer number less than or equal to a. The floor of 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435+\frac{521}{1000} is 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435.

$$139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436-139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435$$

Subtract 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899435 from 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436 to get 1.

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Factor

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